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  "body": "\n## Statement\n\nLet $\\phi(x_1, \\dots, x_n, Y_1, \\dots, Y_m)$ be a formula that quantifies only over sets and contains no free variables other than $x_1, \\dots, x_n, Y_1, \\dots, Y_m$ (not necessarily all of these). Then for all $Y_1, \\dots, Y_m$, there exists a unique class $A$ of $n$-tuples such that:\n\n$$\\forall x_1 \\cdots \\,\\forall x_n [(x_1, \\dots , x_n) \\in A \\iff \\phi(x_1, \\dots, x_n, Y_1, \\dots, Y_m)].$$\n\nThe class $A$ is denoted by $\\{(x_1, \\dots , x_n): \\phi(x_1, \\dots, x_n, Y_1, \\dots, Y_m)\\}.$\n",
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        "locator": "Von Neumann–Bernays–Gödel set theory, section Axiomatization of NBG \u003e Class existence theorem",
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  "name": "Class existence theorem",
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