He's wrong...but so are you.
Once again,
Into the Night is correct and you err.
Axioms, the foundational statements of a closed system, are always held to be self evident and thus are always assumed to be TRUE in all arguments/theorems of that system such that they do not even need to be mentioned. Postulates, on the other hand, are only considered TRUE in those arguments in which they are postulated.
There is a school of thought (to which I subscribe) that holds that once a theorem is proven, it becomes an axiom, i.e. the original axioms are sort of the "null axioms" and proven theorems become "derived axioms" that don't need to be proven again and again and again. They only need to be proven once and they hold true in all arguments of that system, just as the null axioms, with the only difference being that they still need to be cited/mentioned when supporting an argument whereas null-axioms do not.
Cypress' problem (in this particular case) is that he doesn't understand logic, math, or "closed functional systems." He believes that abruptly switching from one closed functional system to another is somehow valid. He believes that
Into the Night is somehow mistaken about Euclidean geometry by mentioning that there exist non-Euclidean geometries. Cypress isn't even courteous enough to credit me for having originally taught him about non-Euclidean geometries.
Don't be afraid to come to me with the hard stuff.