Full Idea
One version of the Axiom of Choice says that for every set A of nonempty sets, there is a function whose domain is A and whose value, for every a ∈ A, is a member of a.
Gist of Idea
Axiom of Choice: some function has a value for every set in a given set
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 1)
Book Reference
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.24