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  "body": "\n## Statement\n\nLet $\\psi (x, y_1, \\dots , y_n)$ be any formula with free variables $x, y_1, \\dots , y_n$.\n\nThen there is a formula $\\varphi (y_1, \\dots y_n)$ with free variables $y_1, \\dots , y_n$ such that for all $m_1 , \\dots , m_n \\in \\mathbb{N}$, $T \\vdash \\varphi (\\overline{m_1} , \\dots , \\overline{m_n}) \\leftrightarrow \\psi (\\ulcorner \\varphi (\\overline{m_1} , \\dots , \\overline{m_n}) \\urcorner, \\overline{m_1} , \\dots , \\overline{m_n})$.\n",
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        "locator": "Diagonal lemma, section Some generalizations \u003e Uniform diagonal lemma",
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  "name": "Uniform diagonal lemma",
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