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20 lines
889 B
20 lines
889 B
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\setlength\subproofhorizspace{1.3em}
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\begin{logicproof}{2}
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\exists x \;(P(x) \lor Q(x)) & prem.\\
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\begin{subproof}
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\llap{$x_0\enspace \;$} P(x_0) \lor Q(x_0) & ass.\\
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\begin{subproof}
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P(x_0) & ass.\\
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\exists x \; P(x) &$ \exists\mathrm{i} 3$\\
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\exists x \; P(x) \lor \exists x \; Q(x) &$ \lor\mathrm{i} 4$
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\end{subproof}
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\begin{subproof}
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Q(x_0) & ass.\\
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\exists x \; Q(x) &$ \exists\mathrm{i} 6$\\
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\exists x \; P(x) \lor \exists x \; Q(x) &$ \lor\mathrm{i} 7$
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\end{subproof}
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\exists x \;P(x) \lor \exists x \; Q(x) &$ \lor\mathrm{e} 2,3-8$
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\end{subproof}
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\exists x \;P(x) \lor \exists x \; Q(x) & $\exists\mathrm{e} 1,2-9$
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\end{logicproof}
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