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18 lines
707 B
18 lines
707 B
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\begin{logicproof}{2}
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\exists x \; (Q(x) \imp R(x)) &\prem \\
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\exists x \; (P(x)\land Q(x)) &\prem \\
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\begin{subproof}
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Q(x_0) \imp R(x_0) &\assum~\freshVar{$x_0$} \\
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\begin{subproof}
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P(x_0) \land Q(x_0) &\assum~\freshVar{$x_0$}\\
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P(x_0) &\ande{1} 4\\
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Q(x_0) &\ande{2} 4\\
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R(x_0) &\impe 5,3\\
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P(x_0) \land R(x_0) & \andi 5,7\\
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\exists x (P(x) \land R(x)) & \existi 8
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\end{subproof}
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\exists x \; (P(x) \land R(x)) & \existe 2,4-9
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\end{subproof}
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\exists x \; (P(x) \land R(x)) & \existe 1,3-10
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\end{logicproof}
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