PHILADELPHIA—Billionaire businessman Michael Bloomberg delivered a stinging rebuke of GOP presidential nominee Donald Trump at the Democratic National Convention Wednesday night, calling him a “dangerous demagogue.”

“Trump says he wants to run the nation like he runs his business. God help us,” said Mr. Bloomberg, a former New York City mayor who is unaffiliated with any political party. “I’m a New Yorker. I know a con when I see one.”

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