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It was the sweaty, heart-pounding first daughters' reunion that wasn't.

Chelsea Clinton and Jenna Bush both felt the burn at the same spin class at SoulCycle in NYC July 26 -- but the fellow Presidential progeny (one Democrat, one Republican) had zero interaction, a witness tells Us Weekly.

But it wasn't intentional. The fitness-minded former White House denizens -- who've remained friendly over the years -- entered the crowded, dark studio separately and "sat on bikes on opposite ends of the room," the witness says.

Business consultant Clinton, 31, just celebrated her one-year wedding anniversary to hubby Marc Mezvinsky, whom she wed in bucolic Rhinebeck, New York on Aug. 1, 2010. Today Show correspondent Bush, 29, celebrated two years of wedded bliss with Henry Hager in May.