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12 lines
699 B
12 lines
699 B
\setlength\subproofhorizspace{1.1em}
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\begin{logicproof}{1}
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\forall a \forall b \; (P(a) \land Q(b)) & prem.\\
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\begin{subproof}
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\llap{$t\enspace \;$} \forall b \; (P(s) \land Q(b)) & $\forall \mathrm{e}$ 1\\
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P(s) \land Q(t) & $\forall \mathrm{e}$ 2\\
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P(s) & $\land \mathrm{e}_1$ 3\\
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P(s) \lor Q(t) & $\lor \mathrm{i}_1$ 4\\
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\exists b \; (P(s) \lor Q(b)) & $\exists \mathrm{i}$ 5
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\end{subproof}
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\forall a \exists b \; (P(a) \lor Q(b)) & $\forall \mathrm{i}$ 2-6
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\end{logicproof}
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