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  "body": "\n## Definition\n\nLet $\\varphi$ and $\\psi$ be formulas of [[propositional logic|09K9MWD2QQ]].\nThe formulas $\\varphi$ and $\\psi$ are logically equivalent when they have the same truth value for each assignment of truth values to their variables.\nThis is written $\\varphi \\equiv \\psi$.\n\n## Remarks\n\nThe formulas $\\varphi$ and $\\psi$ are logically equivalent exactly when $\\varphi \\leftrightarrow \\psi$ is a [[tautology|0D1AHYPM8N]].\nFor example, $p \\to q \\equiv \\neg p \\lor q$.\n[[De Morgan's laws|09PKJKA6J0]] give two more examples.\n\n## Explanations\n\n### L1 human\n\nLogically equivalent formulas say the same thing in different words.\nYou can check an equivalence with a [[truth table|05RSK4Q657]]: the two columns must agree in every row.\nThen you can replace one formula by the other in a proof.\n",
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