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.