Full Idea
Axiom of Choice: ∀A ∃R (R well-orders A). That is, for every set, there must exist another set which imposes a well-ordering on it. There are many equivalent versions. It is not needed in elementary parts of set theory.
Gist of Idea
Choice: ∀A ∃R (R well-orders A)
Source
Kenneth Kunen (Set Theory [1980], §1.6)
Book Reference
Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.15