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NEW YORK — Rafael Nadal kept pulling away in his US Open quarterfinal, then getting reeled back in by Diego Schwartzman.

In the first set, Nadal led 4-0 before Schwartzman got to 4-all. In the second, Nadal went up 5-1 before Schwartzman made it 5-all.

Took more than two hours just for those two sets. Eventually, both were claimed by Nadal. And so, ultimately, was the match and a berth in a 33rd Grand Slam semifinal for Nadal, who prevented Schwartzman from reaching his first by winning 6-4, 7-5, 6-2 after 12:30 a.m. Thursday in Arthur Ashe Stadium.

Roger Federer and Novak Djokovic are both out of the bracket, but Nadal is still around, meaning at least one member of the Big Three is in the semis at a 62nd consecutive major tournament. That trio has combined to win the last 11 Slam trophies — and Nadal is going to be heavily favored to make that 12.

None of the other men left has played in a major final, let alone won one. Nadal, though, is closing in on a fourth championship at the US Open and his 19th at all majors, which would move him only within one of Federer’s record for men.

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On Friday, Nadal will play No. 24 Matteo Berrettini, a 23-year-old from Rome who is Italy’s first male semifinalist in New York since 1977. Berrettini barely got there, edging No. 13 Gael Monfils 3-6, 6-3, 6-2, 3-6, 7-6 (5) on Wednesday.

The other men’s semifinal will be No. 5 Daniil Medvedev of Russia vs. 78th-ranked Grigor Dimitrov of Bulgaria.

In the women’s semifinals Thursday, Serena Williams meets No. 5 Elina Svitolina of Ukraine, and No. 13 Belinda Bencic of Switzerland takes on No. 15 Bianca Andreescu of Canada.

Dimitrov won a five-setter Tuesday night against Federer, who was hampered by an issue with his upper back. Medvedev won his quarterfinal in four sets against Stan Wawrinka, who had built a big lead in the fourth round against Djokovic when the defending champion stopped because of pain in his left shoulder.

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A year ago, it was Nadal whose body broke down: He retired from his semifinal against runner-up Juan Martin del Potro because of a bad knee.

This time, on a muggy night with the humidity above 50%, the lefthander raised some concern by having a trainer come out to rub a cream into that forearm during a changeover early in the third set. At the next changeover, Nadal flexed his right forearm and was visited again by the trainer, took a salt pill and guzzled some drinks, then shook that arm between points in the following game.

Whatever might have been wrong, Nadal managed to play his best when it mattered the most against the 20th-seeded Schwartzman, an Argentine serenaded by loud choruses of ‘‘Olé! Olé! Olé! Olé!’’ by an audience that included former San Antonio Spurs star Manu Ginobili.

Nadal came up with a service break in the last game of each of the opening two sets, then the last one he would need made it 4-2 in the third and he broke yet again to end it.

Now Nadal becomes Berrettini’s problem.