Axiom:Axiom of Choice/Formulation 4

Axiom
Let $A$ be a non-empty set.

Then there exists a mapping $f: \powerset A \to \powerset A$ such that:
 * for every proper subset $x$ of $A$: $\map f x = x$

where $\powerset A$ denotes the power set of $A$.

Also see

 * Equivalence of Formulations of Axiom of Choice