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\setlength\subproofhorizspace{1.1em}\begin{logicproof}{1} \forall a \forall b \; (P(a) \land Q(b)) & prem.\\ \begin{subproof} \llap{$t\enspace \;$} \forall b \; (P(s) \land Q(b)) & $\forall \mathrm{e}$ 1\\ P(s) \land Q(t) & $\forall \mathrm{e}$ 2\\ P(s) & $\land \mathrm{e}_1$ 3\\ P(s) \lor Q(t) & $\lor \mathrm{i}_1$ 4\\ \exists b \; (P(s) \lor Q(b)) & $\exists \mathrm{i}$ 5 \end{subproof} \forall a \exists b \; (P(a) \lor Q(b)) & $\forall \mathrm{i}$ 2-6\end{logicproof}
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