Mayor Bloomberg’s going out with one last ban. The City Council, with the administration’s strong backing, is rushing through a law to treat the vapor from e-cigarettes like tobacco smoke under the city’s “Smoke-Free Air Act.” The use of e-cigs, ­a k a “vaping,” would be forbidden in indoor and outdoor locations wherever smoking is banned.

The key idea is that e-cigs somehow facilitate tobacco smoking – but the best evidence suggests the reverse, that they’re mainly useful for (and used by) people trying to quit. So the ban is likely to do harm, not good.

The goal of the Smoke-Free Air Act has always been to reduce exposure to second-hand smoke, and allow people to smoke in fewer places, with the hope that it would cause them to quit. Banning e-cigs helps on neither front.

It won’t cut exposure to secondhand smoke, because there is no smoke — not even any first-hand smoke. And early evidence is that they’re a much more popular way to help people quit smoking than forcing them to stand out in the cold.

Here’s the science so far: A randomized controlled trial, published in the Lancet last month, found that e-cigs were about as effective an aid in quitting as FDA approved nicotine patches.

The study, funded by the Health Research Council of New Zealand, also found that e-cigs have only a few adverse effects — far fewer than tobacco.

The pro-ban side argues that e-cigarettes “normalize” smoking, because people may be confused and think vaping is smoking. That’s nonsense.

Robin Vitale of the American Heart Association summed up the claim at a council hearing this month: “This mimicry of traditional cigarettes, if used indoors where smoking is banned, can easily lead to confusion and confrontation by New York business owners. The potential for this dynamic to weaken the city’s decade-long ban on smoking in workplaces is quite clear and is the greatest motivating factor to support this proposal.”

Actual business owners beg to differ. Andrew Rigie of the New York City Hospitality Alliance, the trade association for restaurants and bars, testified that e-cigarettes have not become an issue of concern among his members.

It seems that regular folks can tell that the blue LED light on the tip of many e-cigs from the red burning ember at the end of real cigarettes. It helps that vapor doesn’t stink the way tobacco smoke does.

Yes, e-cigs somewhat mimic the old “coffin nails” — that’s why they help you quit. Many smokers prefer kicking the habit with a product that looks and feels like a cigarette.

Spike Babian, co-owner of Vape New York, a city “vape shop,” made the clear point, testifying, “We don’t ban water because it looks like vodka.”

City Health Commissioner Tom Farley presented another red herring at the same hearing, hauling out the “gateway” argument: He claimed, with no data to back up the charge, that e-cigarette use could lead to smoking. In fact, preliminary studies, as well as empirical evidence, show that e-cigarettes are a major gateway away from smoking.

A study presented at the American Association for Cancer Research meeting in November looked at 1,300 college students, average age 19. Only 43 of those told researchers their first nicotine product was an e-cigarette, and only one of the 43 later switched to cigarettes. The vast majority of the 43 who’d tried an e-cigarette weren’t using nicotine or tobacco when researchers followed up.

“It didn’t seem as though it really proved to be a gateway to anything,” said researcher Theodore Wagener, an assistant professor of general and community pediatrics at the University of Oklahoma Health Sciences Center, in Oklahoma City.

As an ultimate fallback, activists suggest e-cig vapor might be dangerous. But in a study this summer, Drexel University’s Dr. Igor Burstyn found “there is no evidence that vaping produces inhalable exposures . . . that would warrant health concerns by the standards that are used to ensure safety of workplaces.”

Grasping at straws, the ban fans suggest it’s just the prudent thing to do until we have more data. No, the prudent thing to do is to help smokers trying to quit.

Jeff Stier, a National Center for Public Policy Research senior fellow, lives on the Upper West Side.