\begin{logicproof}{0}
 \forall x \; (P(x) \land Q(x))              &prem \\
 P(x_0) \land Q(x_0)                         &$\forall \mathrm{e} 1$ \\
 P(x_0)                                      &$\land \mathrm{e} 2$ \\
 P(x_0) \lor Q(x_0)                          &$\lor \mathrm{i} 3$ \\
 \exists x \; (P(x) \lor Q(x))               &$\exists \mathrm{i} 4$
 \end{logicproof}