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11 lines
488 B
11 lines
488 B
\setlength\subproofhorizspace{1em}
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\begin{logicproof}{1}
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\forall x \; (z=x) \land (f(x) = f(z)) & prem.\\
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(z=y) \land f(y) = f(z) & $\forall \mathrm{e}$ 1\\
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\begin{subproof}
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y=z & ass.\\
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f(y) = f(z) & $\land \mathrm{e}_2$2\\
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\exists x \; f(y) = f(x) & $\exists \mathrm{i}$ 4
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\end{subproof}
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y = z \imp \exists x (f(y) = f(x)) & $\imp \mathrm{i}$ 3-5
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\end{logicproof}
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