In South Carolina, a Republican congressman who voted to impeach Trump loses his primary to a Trump-backed rival.

Representative Tom Rice, a staunch conservative who voted to impeach former President Donald J. Trump for fomenting the Jan. 6 attack on the Capitol, was defeated Tuesday by a Trump-endorsed primary challenger, the first of the 10 House Republicans who backed impeachment to test the will of the primary voters and lose.

Mr. Rice’s loss to State Representative Russell Fry means that half of the 10 Republicans who voted to impeach will not return to Congress next year, and that number is likely to grow. In addition to Mr. Rice, four other House Republicans chose to retire rather than face the pro-Trump core of the Republican electorate.

Mr. Fry put Mr. Rice’s impeachment vote at the center of his campaign in the conservative Seventh Congressional District, which runs along the North Carolina border to the Atlantic Ocean. And Mr. Trump rallied with Mr. Fry by his side.

But Mr. Rice, whose defeat was called by The Associated Press, never shrank from his impeachment vote. “I did it then,” he told The New York Times in an interview last week. “And I will do it tomorrow. And I’ll do it the next day or the day after that. I have a duty to uphold the Constitution. And that is what I did.”

Mr. Fry called the vote a betrayal, writing on his campaign website, in a reference to the nicknames of the district’s river and coastal regions, “Tom Rice broke the trust of the people of the Pee Dee and Grand Strand when he voted to impeach President Donald Trump.”

For all the talk of Mr. Trump’s grip loosening on the party, the defeat of a conservative Republican who almost never strayed from the party orthodoxy will send a message to other Republicans tempted to defy the former president. Representatives Adam Kinzinger of Illinois, Anthony Gonzalez of Ohio, Fred Upton of Michigan and John Katko of New York all retired rather than face the voters after their impeachment decisions.

One Republican impeachment voter appears poised to survive the primary season, Representative David Valadao of California, and others will soon be tested: Liz Cheney of Wyoming, Peter Meijer of Michigan and Dan Newhouse and Jaime Herrera Beutler of Washington, all who face Trump-endorsed Republican challengers.

Mr. Rice became an unlikely hero of the anti-Trump movement, a hard-core conservative who was defiant in his contempt for the former president. When Mr. Trump rallied against him in March, he responded with a statement saying, “Trump is here because, like no one else I’ve ever met, he is consumed by spite. I took one vote he didn’t like and now he’s chosen to support a yes-man who has and will bow to anything he says, no matter what.”

Maya King contributed reporting.