Yankees' Gerrit Cole continues to progress in his rehab 

Gerrit Cole’s rehab can best be described this way: slow but steady.

And most important from his and the Yankees’ perspective?

So far, no setbacks.

The reigning American League Cy Young Award winner, who started the season on the injured list with right elbow inflammation, took his next step – albeit a minor one – Saturday morning, getting two “ups” during a 40-pitch bullpen session. (“Ups” meaning Cole simulated pitching two innings, throwing 20 pitches before sitting down, as he would do between innings of a game, and then throwing 20 more.)

“I thought he was pretty sharp,” pitching coach Matt Blake said. “He keeps progressing. Intensity was pretty good, used all his pitches, had some hitters stand in. Definitely steps forward.”

The next step of significance would be Cole, who is the early stages of what is the equivalent of a six-week spring training to build up for regular-season games, facing hitters in a simulated game, something Blake said could come soon.

“I think that’s a big one for him to check that box,” Blake said of Cole experiencing multiple “innings” in the bullpen. “Now that’s typically a progression where we may just double that up or potentially face some hitters. So we’ll see how he bounces back after today and then go from there.”

In such sessions with an already established big-leaguer, Blake said what he looks for is the “crispness” of the pitches at this stage of his buildup.

“Obviously, it’s still kind of a spring training progression of sorts for him as he’s rehabbing,” Blake said. “Just making sure that the quality of the pitches is getting better each time out and he’s responding well. So far, so good.”

Since Cole was diagnosed with the elbow inflammation in mid-March, the Yankees have not offered a time frame for his return, but all along, the club collectively would have said “where do I sign?” for that occurring by July 1. That date still remains very much in play.

The rest of the rotation, very much to the surprise of many in the organization – including in the dugout – has done far more than merely tread water in Cole’s absence.

Going into Saturday’s 6-1 victory over the White Sox, the Yankees’ rotation had a 3.03 ERA in 46 starts, the second-lowest ERA in the AL and third-lowest in the majors. The Yankees entered Saturday with their starters having lasted at least four innings in each of their outings, with the Orioles the only other team accomplishing that feat.

“They’ve been excellent,’’ manager Aaron Boone said before Friday night’s game, in which Nestor Cortes allowed one run (unearned) in seven innings in a 4-2 victory, making it 37 out of 46 starts in which a rotation member allowed three or fewer earned runs (the group has allowed two or fewer in 29 of those outings and one or fewer in 22). “They’ve given us a chance to win virtually every day, and ultimately that’s what it’s all about. They’ve done it consistently and they’ve done it well.”

Extra bases

Jose Trevino, who went 1-for-4, including his fifth homer, has three homers in his last four games. The catcher is slashing .348/.371/.576 with five homers, 14 RBIs and 12 runs in his last 22 games . . . Juan Soto (4-for-4 with two homers and a walk) has reached base in 41 of his 47 games. He has reached base three times in 15 of those games, the most such games in the majors this season . . . The Yankees have won 12 of their first 15 series for the second time in the last 75 seasons (since 1950), the last time coming in 2002. They also accomplished the feat in 1928, ’32, ’39 and ’49.