Axiom of power set

Statement

In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set $x$ the existence of a set $\mathcal{P}(x)$, the power set of $x$, consisting precisely of the subsets of $x$. By the axiom of extensionality, the set $\mathcal{P}(x)$ is unique.