Axiom of extensionality in the context of "Axiom of power set"

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

The axiom of power set appears in most axiomatizations of set theory. It is generally considered uncontroversial, although constructive set theory prefers a weaker version to resolve concerns about predicativity.