The Axiom of Choice (a.k.a. AC) is the classiest, most desired axiom of set theory (hence its name). At some point, the other axioms rebelled against it in jealous rage, leaving mathemagicians with no longer any constructive way to use its high-horse results. It now lives independently from those other axioms (if you know what I mean), and prolonged consideration of its truth will probably result in Christians knocking down your door.