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\begin{logicproof}{2}
p \lor q & \prem \\
p \implies r & \prem \\
\lnot s \implies \lnot q & \prem \\
\begin{subproof}
p & \assum \\
r & $\impe 4,2$ \\
r \lor s & $\ori{1} 5$
\end{subproof}
\begin{subproof}
q & \assum \\
s & $\MT 3,7$ \\
r \lor s & $\ori{2} 8$
\end{subproof}
r \lor s & $\ore 1,4-6,7-9$
\end{logicproof}