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14 lines
531 B
14 lines
531 B
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\begin{logicproof}{2}
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\forall x \; (P(x) \land Q(x)) &\prem \\
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\begin{subproof}
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& \freshVar{$x_0$} \\
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P(x_0) \land Q(x_0) & \foralle 1 $x_0$ \\
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P(x_0) & \ande{1}1 \\
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Q(x_0) & \ande{2}1 \\
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R(x_0) \lor P(x_0) & \ori 4 \\
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Q(x_0) \lor R(x_0) & \ori 5 \\
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(Q(x_0) \lor R(x_0)) \land (R(x) \lor P(x)) & \andi 6,7
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\end{subproof}
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\forall x \; ((Q(x) \lor R(x)) \land (R(x) \lor P(x))) & \foralli 2-8
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\end{logicproof}
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