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\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}
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