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14 lines
615 B
14 lines
615 B
\setlength\subproofhorizspace{1.3em}
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\begin{logicproof}{2}
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\forall x \; \lnot (P(x) \land Q(x)) & prem.\\
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\begin{subproof}
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\exists x \; (P(x) \land Q(x)) & ass.\\
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\begin{subproof}
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\llap{$t\enspace \;$} P(t) \land Q(t) & ass.\\
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\lnot P(t) \land Q(t) & $\forall \mathrm{e}$ 1\\
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\bot & $\lnot \mathrm{e}$ 3,4
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\end{subproof}
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\bot & $\exists \mathrm{e}$ 3-5
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\end{subproof}
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\lnot \exists x \; (P(x) \land Q(x)) & $\lnot \mathrm{i}$ 2-6
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\end{logicproof}
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