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21 lines
621 B
21 lines
621 B
This sequent is provable.
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\begin{logicproof}{2}
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\begin{subproof}
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p \imp (q \land r) & \assum \\
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\begin{subproof}
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p & \assum \\
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q \land r & $\impe 1,2$\\
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q & $\ande{1} 3$
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\end{subproof}
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p \imp q & $\impi 2-4$ \\
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\begin{subproof}
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p & \assum \\
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q \land r & $\impe 1,6$ \\
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r & $\ande{2} 7$
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\end{subproof}
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p \imp r & $\impi 6-8$ \\
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(p \imp q) \land (p \imp r) & $\andi 5,9$
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\end{subproof}
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(p \imp (q \land r)) \imp ((p \imp q) \land (p \imp r)) & $\impi 1-10$
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\end{logicproof}
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