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15 lines
544 B
15 lines
544 B
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\begin{logicproof}{2}
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\forall 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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P(x_0) \land Q(x_0) & \assum~\freshVar{$x_0$}\\
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Q(x_0) \imp R(x_0) & \foralle 1 $x_0$\\
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P(x_0) & \ande{1} 3 \\
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Q(x_0) & \ande{2} 3 \\
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R(x_0) & \impe 6,4\\
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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 2,3-9
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\end{logicproof}
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