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  "body": "\n## Summary\n\nA proof system is sound when everything it proves is true.\nMore precisely, whenever $\\Gamma \\vdash \\varphi$ in the system, also $\\Gamma \\models \\varphi$ as a [[logical consequence|1HK0VYWTV7]].\nSoundness is the converse of completeness, and the standard proof systems for propositional and first-order logic have both.\nA sound system can never prove a false statement from true premises.\n\n## Explanations\n\n### L1 human\n\nA proof system is sound if its rules never lead from true premises to a false conclusion.\nFor example, modus ponens is a safe rule: if $p$ and \"if $p$ then $q$\" are true, then $q$ is true.\nA rule such as \"from $q$ and if $p$ then $q$, infer $p$\" is unsafe, because $q$ may be true while $p$ is false.\nIn philosophy, an argument is also called sound when it is valid and all its premises are true.\n",
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