The five cops of the plainclothes anti-crime unit at the 46th Precinct in the Bronx were just going off duty and doffing their bulletproof vests when they heard a radio report of an armed robbery at a grocery a few blocks from the station house.

Their immediate response tells an important truth about a police slowdown that has spread throughout New York City in recent days.

As anyone could surmise, the slowdown was born of grief over the loss of two cops, anger at a mayor widely viewed in the department as unsupportive and fatigue from anti-cop demonstrations.

That, and so much overtime from policing the protests that many cops had reached another limit—their individual allotment of what they can take in cash rather than time. Cops generally do not like busting people for petty offenses anyway, and they like it even less when it adds nothing to their paychecks.

The result has been a precipitous decline in summonses and arrests for minor crimes in every precinct in the city, including the 46th.

But when it comes to a truly serious crime such as an armed robbery, cops across the city would do just what the anti-crime squad did in the Bronx on Monday night even though their tour was officially done.

They all immediately dashed out to their car to catch the bad guys.

These were cops who had worked the protests and suffered the accompanying verbal taunts and abuse.

They had also attended the funerals for the two officers who were murdered in Brooklyn on December 20.

And they did not even pause to don their bulletproof vests lest that one instant be the instant that allowed the robbers to get away.

The patrol sergeant reported over the radio that the two masked robbers had already fled the premises. The anti-crime cops began searching the likely path of flight. They were looping back around and coming down Tiebout Avenue when they spotted two figures.

The description of the robbers was of one man in a distinctive green-and-brown parka and another in a black coat and gray sweatpants. The clothing of these men did not match, but the suspicions of the cops were aroused when one of the men ducked into a Chinese takeout restaurant upon seeing their unmarked car come down the block.

The cops climbed out and approached the man who remained in the street. The man inside was at the counter, ordering a Snapple, when he suddenly whirled around and fired a long-barreled .44 magnum revolver through the restaurant’s front window.

The big slug happened to hit the suspect in the street, passing through his arm and then striking Police Officer Andrew Dossi.

The gunman then burst from the restaurant and fled down the street with the other man. The cops gave chase and the gunman fired the big revolver twice more.

“You can imagine the sound of that gun on a Bronx street,” Chief of Detectives Robert Boyce says.

A second cop, Officer Aliro Pellerano, also was wounded. One of the other cops fired three times and those who were still able to give chase did. They saw the gunman hijack a white Camaro that he would crash a few blocks away, discarding the revolver as he got away. The wounded suspect managed to escape on foot.

At St. Barnabas Hospital, Pellerano was listed in stable condition with wounds to his chest and arm. Dossi initially was listed in critical condition with wounds to his arm and lower back. A nurse called his parents’ home. The mother answered and became frantic. The father picked up, not knowing what it was about.

“I heard them say, ‘He was shot twice,’” the father, Joseph Dossi, remembers.

The father understood immediately that it must be his son.

“He’s the only person I know who would get shot,” the father says.

When the father arrived at the hospital, he was told that Andrew Dossi was in surgery, but the wounds were not life-threatening. Andrew had survived two tours with the Army airborne in Iraq and was scheduled to be deployed as a reservist to Africa just next week. But that would now have to be put on hold because he had been shot in the Bronx.

Police Commissioner William Bratton arrived. He made clear that he fully appreciated what the cops had done.

“He said they went back out, they didn’t have to, they were done with their tour,” the father reports.

About an hour later, Mayor Bill De Blasio appeared. He was getting another lesson in what he had seemed not to appreciate fully about cops. He appeared to understand however belatedly that he was in the presence of another kind of greatness.

“He was very humble,” the father says. “He acted like he was very concerned. He listened to any word I said and Bratton said. To me he acted the way I would think he should act.”

What spoke loudest to the whole city was the devotion these cops had shown by racing into danger when they were supposed to be done for the day. The NYPD released a photo of the gunman taken from a surveillance camera in the Chinese restaurant and received 29 calls on its tips line. Ten of the callers identified the man as Jason Polanco of the Bronx.

In the meantime, detectives were interviewing a man who had appeared with a gunshot wound at Columbia-Presbyterian Hospital in Upper Manhattan roughly a half hour after the shooting. The man, Joshua Kemp, told what police describe as “a bogus story that quickly fell apart.” He proved to be on parole for robbery and to be listed as a member of the DDP gang in the Bronx.

“We saw his background and he was a Bronx guy and we started breaking the case,” Boyce says.

The police learned that Kemp worked in a grocery on Decatur Avenue. His boss there told them that a wounded Kemp had come running in shortly after the time of the shooting and disappeared into the back with a black duffel bag similar to the one the robbers had used to stuff the loot from the other grocery.

“I got robbed! I need to go to the hospital!” he supposedly cried out to his boss.

There remained a discrepancy between what the masked suspects can be seen wearing in the surveillance video of the robbery and their clothing when the anti-crime cops spotted them. The detectives wondered at first if the gunman and his pal had been involved in some other crime unrelated to the grocery stick-up. They then discovered that attire matching the original description had been discarded along the path from the robbery to the scene of the shooting.

Kemp was arrested. Polanco, the suspected gunman, was still at large as the year’s first snow muffled the Bronx. The searchers included an NYPD bloodhound named Bella, trailed through the swirling flakes by a handler as well as helmeted Emergency Service Unit cops with a ballistic shield and an automatic weapon.

Detectives with a fugitive task force caught up with Polanco and a friend on a Bronx street in the early afternoon. Boyce was asked at a press conference if Polanco went peacefully.

“Peacefully? No,” Boyce said.

Surveillance video of the robbery at the Welcome 2 Yemen grocery shows the man police say is Polanco pointing the big revolver at a customer and a bread-delivery man, forcing them to sprawl on the floor. The robber police say is Kemp hops the counter brandishing a knife and stuffs the cash into a black duffel bag as the 20-year-old cashier sits with both hands raised.

“He told me, ‘Give me the rest of the money!’” recalls the cashier, Mooreldin Algabyali.

After the robbers flee, the bread-delivery man can be seen helping the customer to his feet. The cashier grabs a phone and makes the call to 911 that would soon after prompt the anti-crime cops to hurry into harm’s way despite all that has happened in recent weeks.

As captured by the outside surveillance video, the pair turned up East 180th Street, across from Public School 163, the flag outside at half-staff in memory of the cops who were murdered in Brooklyn just before Christmas.

The robbers then turned up Tiebout Avenue, discarding the green-and-brown coat and other garments along the way. Surveillance video outside the Chinese restaurant shows the cops approach the one who remains in the street while the other goes inside. The interior video shows the gunman firing the shot through the window.

When the crime scene tape was taken down late Tuesday morning, the resulting bullet hole in the Plexiglas gave continued testament to what the cops were risking; to how close this patch of pavement came to being another place in the city where a police officer made the ultimate sacrifice.

Around the corner from the shooting scene was a mural to a neighborhood resident who was killed back in 1994, when the cops were just beginning to transform New York from a war zone into the safest big city in America. A passing off-duty school safety officer named Fred Lucas said that he had been told the man was a drug dealer.

Lucas is well aware that one of the officers murdered in Brooklyn, Rafael Ramos, had been a school safety officer before joining the NYPD. Lucas said that he himself nonetheless hopes to become a cop.

“I’m not scared,” he said as he stood a few feet from the previous night’s shooting of two cops.

Lucas answered immediately when asked why he wanted to join the NYPD.

“Saving the lives of others,” he said.

Nobody ever says they want to become a cop so they can bust people for urinating in public or drinking alcohol on their stoop.

Many of those who have become cops in New York seem to have ceased to address such minor offenses over the past few days. The judges who handle arraignments at criminal court in all five boroughs have a small fraction of their usual caseloads.

“There’s no work,” a court officer said Monday night.

The slowdown may continue for a time, though if it goes on too long, Bratton has pledged to identify the particular officers and address the problem “appropriately and effectively.”

One supervisor suggests that the situation may begin to rectify itself as overtime allotments are renewed and mortgage payments become due.

Anybody who worries for the city’s safety can find reassurance in those five anti-crime cops in the 46th Precinct, who did what all cops do when being true to why they became cops in the first place. Bronx Criminal Court may be way down in quality-of-life cases, but the few arrestees who do appear will include Kemp, charged with robbery, and Polanco, charged with robbery and attempted murder of a police officer.

The father of the wounded Officer Andrew Dossi sums it up perfectly.

“They did the right thing,” Joseph Dossi says. “Unfortunately, somebody got shot.”