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  "body": "\n## Summary\n\nIn mathematical logic, a set $\\mathcal{T}$ of logical formulae is **deductively closed** if it contains every formula $\\varphi$ that can be logically deduced from $\\mathcal{T}$; formally, if $\\mathcal{T} \\vdash \\varphi$ always implies $\\varphi \\in \\mathcal{T}$. If $T$ is a set of formulae, the **deductive closure** of $T$ is its smallest superset that is deductively closed.\n",
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