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It began with Sean Hannity introducing Mayor Bill de Blasio as the “far left” mayor, only to offer a better gibe: “Comrade de Blasio.”

For the next 41 minutes — twice as long as planned — Mr. Hannity and the mayor sparred on Mr. Hannity’s show on Fox News on Wednesday night, over everything from immigration and gun control to abortion and meatless Mondays in New York City’s schools.

It was the first time a 2020 Democratic presidential candidate had appeared on the show, “Hannity,” and neither man could contain their apparent glee at the opportunity the appearance afforded them.