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16 lines
989 B
16 lines
989 B
\setlength\subproofhorizspace{1.1em}
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\begin{logicproof}{1}
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\exists x \forall y \; (P(y) \imp Q(x)) & prem.\\
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\forall s \; \lnot Q(s) \land R(s) & prem.\\
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\begin{subproof}
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\llap{$t\enspace \;$} \forall y \; (P(y) \imp Q(t)) & ass.\\
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P(t) \imp Q(t) & $\forall \mathrm{e}$ 3\\
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\lnot Q(t) \land R(s) & $\forall \mathrm{e}$ 2\\
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\lnot Q(t) & $\land \mathrm{e}_1$ 5\\
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\lnot P(t) & MT 4,6\\
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\exists x \; \lnot P(t) & $\exists \mathrm{i}$ 7\\
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\lnot R(s) & $\land \mathrm{e}_2$ 5\\
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R(s) \imp \exists x \; \lnot P(t) & $\exists \mathrm{i}$ 7\\
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\end{subproof}
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R(s) \imp \exists x \; \lnot P(t) & $\exists \mathrm{e}$ 3-10
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\end{logicproof}
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