Axiom:Axiom of Powers

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

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

Otherwise known as the Axiom of the Power Set.