\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} 