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14 lines
700 B
14 lines
700 B
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\setlength\subproofhorizspace{1.3em}
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\begin{logicproof}{1}
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\exists 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) & ass.\\
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P(x_0) & $\land\mathrm{e} 2$\\
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Q(x_0) & $\land\mathrm{e} 2$\\
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\exists x \; P(x) & $\exists\mathrm{i} 3$\\
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\exists x \; Q(x) & $\exists\mathrm{i} 4$\\
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\exists x \; P(x) \land \exists \; Q(x) & $\land\mathrm{i} 5,6$
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\end{subproof}
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\exists x \;P(x) \land \exists x \; Q(x)) & $\exists\mathrm{e} 1,2-7$
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\end{logicproof}
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