\setlength\subproofhorizspace{1.7em}
\begin{logicproof}{1}
  \forall x \;( P(x) \land  Q(x) )    & prem.\\
  \begin{subproof}
    \llap{$x_0\enspace \;$} P(x_0) \land Q(x_0) & $\forall \mathrm{e}$ 1\\
    P(x_0)                                  & $\land \mathrm{e}$ 2
  \end{subproof}
  \forall x \; P(x)                       & $\forall \mathrm{i} 2-3$\\
  \begin{subproof}
    \llap{$x_1\enspace \;$} P(x_1) \land Q(x_1) & $\forall \mathrm{e}$ 1\\
    Q(x_1)                                  & $\land \mathrm{e}$ 5
  \end{subproof}
  \forall x \; Q(x)                       & $\forall \mathrm{i} 5-6$\\
  \forall x \; P(x) \land \forall x \; Q(x) & $\land \mathrm{i}$ 4,7
\end{logicproof}