Axiom:Axiom of Choice/Formulation 4

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Let $A$ be a non-empty set.

Then there exists a mapping $f: \powerset A \to A$ such that:

for every non-empty proper subset $x$ of $A$: $\map f x \in x$

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

Also see

  • Results about the Axiom of Choice can be found here.