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\setlength\subproofhorizspace{1em}
\begin{logicproof}{2}
\exists x \; (P(x) \imp Q(y)) & prem.\\
\forall x \; P(x) & prem.\\
\begin{subproof}
\llap{$x_0\enspace \;$} P(x_0) \imp Q(y) & ass.\\
P(x_0) & $\forall \mathrm{e}$ 2\\
Q(y) & $\imp \mathrm{e}$ 3,4
\end{subproof}
Q(y) & $\exists \mathrm{e}$ 3-5
\end{logicproof}