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