If you let me define the axiom system, I can make 2+2 equal anything you want. I can make it equal 0 quite easily, in fact. I’m not saying the resulting axiom system would be interesting or useful to you or anyone else, but I can do it, and the equality would be perfectly true within that axiom system.
My point is that axiom systems allow us to derive truths, but they are only true within the axiom system from which they are derived; they may be false or meaningless in other axiom systems, and are only relevant to the outside world as descriptions or models of physical relationships and processes. However, something that is true within an axiom system is always and absolutely true within that axiom system. That kind of absoluteness is not available to us in the physical world.