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\begin{logicproof}{2}
q \imp r & \prem \\
\begin{subproof}
p \lor q & \assum\\
\begin{subproof}
p & \assum \\
p \lor r & $\ori{1} 2$
\end{subproof}
\begin{subproof}
q & \assum \\
r & $\impe 5,1$ \\
p \lor r & $\ori{2} 6$
\end{subproof}
p \lor r & $\ore 2,3-4,5-7$
\end{subproof}
p \lor q \imp (p \lor r) &$\impi 2-8$
\end{logicproof}