---
tag: Z35WXSBYM7
kind: statement
role: proposition
name: Axiom of power set
aliases: [axiom-of-powerset, axiom-of-the-power-set, axiom-power-set, axiom-powerset, power-set-axiom, powerset-axiom]
sources:
  - wikipedia: en:52552@r1325037263
    locator: Axiom of power set
    note: adopted
    mention: wikipedia://en/52552
    sections: [Statement]
same_as:
  wikidata: Q1077811
  wikipedia: Axiom of power set
inventory: [FVZH3BH74M]
---

## 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|00E0YZCERH]] of $x$, consisting precisely of the [[subsets|0BJR9QR08E]] of $x$. By the [[axiom of extensionality|0TB16T2C97]], the set $\mathcal{P}(x)$ is unique.