# Axiom:Axiom of Powers/Set Theory

## Axiom

For every set, there exists a set of sets whose elements are all the subsets of the given set.

$\forall x: \exists y: \paren {\forall z: \paren {z \in y \iff \paren {w \in z \implies w \in x} } }$

## Also known as

The axiom of powers is also known as the axiom of the power set.