Questionnaire-2024/natural_deduction_propositional_logic/0022_sol.tex

\begin{logicproof}{2}
		p \implies q & \prem \\
		p \land (r \lor q) & \prem \\
		\begin{subproof}
			q \implies p & \assum \\
			r \lor q & $\ande{2} 2$ \\
			p & $\ande{1} 2$ \\
			q & $\impe 1,5$ \\
      (s \land t) \lor q & $\ori{2} 6$ \\
			((s \land t) \lor q) \land (r \lor q) & $\andi 7,4$
		\end{subproof}
		(q \implies p) \implies ((s \land t) \lor q) \land (r \lor q) & $\impi 3-7$
	\end{logicproof}