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  "body": "\n## Summary\n\nModus ponens is the rule of inference that gets $q$ from the two premises $p$ and $p \\to q$.\n$$\\frac{p \\qquad p \\to q}{q}$$\nIt is valid: when the two premises are true, the conclusion $q$ is true.\n\n## Remarks\n\nMost proof systems for [[propositional logic|09K9MWD2QQ]] use modus ponens as a rule.\nIts partner modus tollens gets $\\neg p$ from $\\neg q$ and $p \\to q$.\n\n## Explanations\n\n### L1 human\n\nModus ponens is the most common step in a proof.\nIf you know that $n$ is divisible by $4$, and that each number divisible by $4$ is even, then you know that $n$ is even.\n",
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