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23 lines
649 B
23 lines
649 B
\begin{logicproof}{2}
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q \lor \lnot q & $\LEM$ \\
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\begin{subproof}
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q & \assum\\
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\begin{subproof}
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p & \assum\\
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q & $\copying 2$
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\end{subproof}
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p \imp q & $\impi 3-4$ \\
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(p \to q) \lor (q \to r) & $\ori{1} 5$
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\end{subproof}
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\begin{subproof}
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\lnot q & \assum\\
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\begin{subproof}
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q & \assum\\
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\bot & $\nege 7,8$ \\
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r & $\bote 9$
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\end{subproof}
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q \imp r & $\impi 8-10$ \\
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(p \imp q) \lor (q \imp r) & $\ori{2} 11$
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\end{subproof}
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(p \to q) \lor (q \to r) & $\ore 1, 2-6,7-12$
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\end{logicproof}
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