From bodegas, to pizzerias, to high-end restaurants, the city’s Board of Health voted yesterday morning to make New York the first city in the nation to ban trans fats.

The board, which passed the ban unanimously, did give restaurants a slight break by relaxing what had been considered a tight deadline for compliance. Restaurants will be barred from using most frying oils containing artificial trans fats by July and will have to eliminate the artificial trans fats from all of their foods by July 2008.

But restaurant industry representatives called the ban burdensome and unnecessary.

”We don’t think that a municipal health agency has any business banning a product the Food and Drug Administration has already approved,” said Dan Fleshler, a spokesman for the National Restaurant Association.

The ban contains some exceptions; for one, it would allow restaurants to serve foods that come in the manufacturer’s original packaging.

Trans fats are believed to be harmful because they contribute to heart disease by raising bad cholesterol and lowering good cholesterol at the same time. Some experts say that makes trans fats worse than saturated fat.

The panel also passed another measure that has made restaurants unhappy: Some that choose to inform customers about calorie content will have to list the information right on the menu. The rule would generally apply to fast-food restaurants and other major chains.

Sheila Weiss, director of nutritional policy for the restaurant association, said the rule would be a disincentive for restaurants to provide any nutritional information.

Trans fats are formed when liquid oils are made into solid fats by adding hydrogen in a process called hydrogenation. A common example of this is partially hydrogenated vegetable oil, which is used for frying and baking and turns up in processed foods like cookies, pizza dough and crackers. Trans fats, which are favored because of their long shelf life, are also found in premade blends like pancake and hot chocolate mix.

The FDA estimates the average American eats 4.7 pounds of trans fats each year.

Mayor Michael Bloomberg, who banned smoking in bars and restaurants during his first term, has dismissed cries that New York is crossing a line by trying to legislate diets.

”Nobody wants to take away your french fries and hamburgers — I love those things, too,” he said recently. “But if you can make them with something that is less damaging to your health, we should do that.”

Many food makers have stopped using trans fats on their own after the FDA began requiring companies to list trans fat content on labels.

McDonald’s Corp. has been experimenting with more than a dozen healthier oil blends but has not committed to a full switch. At an investor conference last month, CEO Jim Skinner said the company is making ”very good progress,” at developing an alternative, and vowed to be ready for a New York City ban.

Wendy’s International Inc. introduced a zero-trans fat oil in August, and Yum Brands Inc.’s KFC and Taco Bell said they also will cut trans fats.