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Judge Neil M. Gorsuch was confirmed by the Senate on Friday to become the 113th justice of the Supreme Court, capping a political brawl that lasted for more than a year and tested constitutional norms inside the Capitol’s fraying upper chamber.

The development was a signal triumph for President Trump, whose campaign last year rested in large part on his pledge to appoint another committed conservative to succeed Justice Antonin Scalia, who died in February 2016. However rocky the first months of his administration may have been, Mr. Trump now has a lasting legacy: Judge Gorsuch, 49, could serve on the court for 30 years or more.