0.2 Axioms pt.1

Set existence, Extensionality, Pairing and Union Axioms.

notes:

Something to think about:
"∃" means the same thing as "¬∀¬" and
"∀" means the same thing as "¬∃¬"

[llinuxer]

Are the two ways of stating the "axiom of pair set" equivalent?
Looks like the way it is stated in the wiki entry is more restrictive. e.g. given x and y there exists a set containing only x and y {x, y} and no other. I guess both ways of defining this axiom will do the same job in proofs and in other definitions.