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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, contains no free variables other than $x_1, \\dots, x_n, Y_1, \\dots, Y_m$, and may contain relations, special classes, and operations defined by formulas that quantify only over sets. 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",
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    "name": "Class existence theorem (extended version)",
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        "locator": "Von Neumann–Bernays–Gödel set theory, section Axiomatization of NBG \u003e Extending the class existence theorem",
        "mention": "wikipedia://en/528491#2D64",
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  "name": "Class existence theorem (extended version)",
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  "url": "https://math2.tamnd.com/wiki/class-existence-theorem-extended-version/",
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