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  "body": "\n## Proof\n\nWe compare the [[truth tables|05RSK4Q657]] of $\\neg \\neg p$ and $p$.\n\n1. Let $p$ be a [[proposition|0ZGC7ZESYN]]. In classical logic, $p$ is either true or false.\n2. Suppose $p$ is true. By the definition of [[negation|0XR7A7RSXB]], $\\neg p$ is false. Applying the definition again, $\\neg \\neg p$ is true.\n3. Suppose $p$ is false. By the definition of negation, $\\neg p$ is true. Applying the definition again, $\\neg \\neg p$ is false.\n4. The truth table is this.\n\n| $p$ | $\\neg p$ | $\\neg \\neg p$ |\n|---|---|---|\n| T | F | T |\n| F | T | F |\n\n5. By steps 1, 2 and 3, $\\neg \\neg p$ and $p$ have the same truth value for each truth value of $p$.\n6. So $\\neg \\neg p$ and $p$ are [[logically equivalent|06GYGS41JK]], that is, $\\neg \\neg p \\equiv p$.\n\n## Idea\n\nNegation swaps true and false. Swapping twice gives back the original truth value, so $\\neg \\neg p$ always agrees with $p$.\n",
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