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20 lines
662 B
20 lines
662 B
\begin{logicproof}{2}
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(p \implies q)
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\land (q \implies p) & \prem \\
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p \lor \lnot p & $\LEM$ \\
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\begin{subproof}
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p & \assum \\
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p \implies q & $\ande{1} 1$ \\
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q & $\impe 3,4$ \\
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p \land q & $\andi 3,5$ \\
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(p \land q) \lor (\lnot p \land \lnot q) & $\ori{1} 6$
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\end{subproof}
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\begin{subproof}
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\lnot p & \assum \\
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q \implies p & $\ande{2} 1$ \\
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\lnot q & $\MT 8,9$ \\
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\lnot p \land \lnot q & $\andi 8,10$ \\
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(p \land q) \lor (\lnot p \land \lnot q) & $\ori{2} 11$
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\end{subproof}
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(p \land q) \lor (\lnot p \land \lnot q) & $\ore 2,3-7,8-12$
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\end{logicproof}
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