Perhaps to say "valid in any other universe" is a language mismatch, since validity doesn't refer to universes, only to the rules of the system.

Well, what if in some other universe every process isomorphic to a statement "2 + 2" concludes that it equals "3" instead of "4" - would this mean that the abstract fact "2 + 2 = 4" is false/invalid in that universe?

If it concluded 3 instead of 4, it would not be isomorphic to our "2+2". Both systems of mathematics (in our and the other universes) have to be isomorphic as a whole to enable translation between them.