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  "body": "\n## Statement\n\nLet $\\psi (x)$ be any formula in the language of $T$ with only $x$ as free variable. Then there is a term $t$ in the language of $T$ such that $T \\vdash t = \\ulcorner \\psi (t) \\urcorner$.\n\nTrivially, the diagonal lemma follows from the strong diagonal lemma (take $\\varphi (x)$ to be $\\psi (t)$). Note however that the strong diagonal lemma depends on the language of $T$, particularly on whether there is such a term $t$. Typically, the strong diagonal lemma fails for theories in the basic language of arithmetic (such as $\\mathsf{Q}$ or $\\mathsf{PA}$), but holds for primitive recursive arithmetic $\\mathsf{PRA}$ which has a function symbol for each primitive recursive functions.\n",
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