Questionnaire-2024/natural_deduction_predicate_logic/0001_sol.tex

\begin{logicproof}{1}
	\forall x \; \big(P(x) \imp Q(x)\big)			& prem.\\
	\forall x \; P(x) 										& prem.\\
	\begin{subproof}
		\llap{$x_0\quad$} P(x_0) \imp Q(x_0)	& $\forall \mathrm{e}$ 1 \\
		P(x_0)												& $\forall \mathrm{e}$ 2 \\
		Q(x_0)												& $\imp \mathrm{e}$ 3,4
	\end{subproof}
	\forall x \; Q(x)										& $\forall \mathrm{i}$ 3-5
\end{logicproof}