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  "aliases": [
    "axiom-of-powerset",
    "axiom-of-the-power-set",
    "axiom-power-set",
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  "body": "\n## Statement\n\nIn 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.\n",
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