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26x1.25 slick fit on a rim that I now have with a measure on the tire
26x2.00 and the rims I have are
26inch bontrager AT-550?
The Bontrager AT-550 rim is a standard 26" mountain bike rim. A typical MTB 26" tire, including the narrower 1.25" should fit, yes.
You should compare the bead diameter on the original tire to the new tire. it's the three digit number on the tire that matters. Usually, for these tires, it would be 559mm.
You should make sure that the tire width is a minimum of 1/8" or 5mm wider than the width of the rim.