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14 lines
710 B
14 lines
710 B
\begin{logicproof}{1}
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\forall x \; (P(x) \land Q(x)) &prem \\
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\begin{subproof}
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\llap{$x_0\enspace \;$} \: P(x_0) \land Q(x_0) &$\forall \mathrm{e} 1 $\\
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P(x_0) &$\land \mathrm{e} 2$
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\end{subproof}
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\forall x \; P(x) &$\forall \mathrm{i} 2-3 $\\
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\begin{subproof}
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\llap{$x_1\enspace \;$} \: P(x_1) \land Q(x_1) &$\forall \mathrm{e} 1 $\\
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Q(x_1) &$\land \mathrm{e} 5$
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\end{subproof}
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\forall x \; Q(x) &$\forall \mathrm{i} 5-6 $\\
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\forall x \; P(x) \land \forall x \; Q(x) &$\land \mathrm{i} 4,7$
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\end{logicproof}
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