Full Idea
Zermelo has shown that [the Axiom of Choice] is equivalent to the proposition that every class is well-ordered, i.e. can be arranged in a series in which every sub-class has a first term (except, of course, the null class).
Gist of Idea
Choice is equivalent to the proposition that every class is well-ordered
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], XII)
Book Reference
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.123
A Reaction
Russell calls Choice the 'Multiplicative' Axiom.