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The United States House of Representatives voted narrowly on Tuesday to impeach Alejandro N. Mayorkas, the homeland security secretary, in a precedent-shattering vote that charged him with willfully refusing to enforce border laws and breaching the public trust.

In a 214-to-213 vote, Republicans barreled past the solid opposition of Democrats and reservations in their own ranks to make Mr. Mayorkas the first sitting cabinet secretary in U.S. history to be impeached.