Axiom:Axiom of Powers

Axiom

For every set, there exists a collection of sets that contains amongst its elements all the subsets of the given set.

$\forall x: \exists y: \left({\forall z: \left({z \in y \iff \left({w \in z \implies w \in x}\right)}\right)}\right)$

Otherwise known as the Axiom of the Power Set.

Also see

• Power Set

Sources

• Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 5$: Complements and Powers

• Weisstein, Eric W. "Zermelo-Fraenkel Axioms." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html