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\begin{logicproof}{1}
p \imp q & \prem \\
q \imp r & \prem\\
\begin{subproof}
p & \assum\\
q & $\impe 3,1$\\
r & $\impe 4,2$
\end{subproof}
p \imp r & $\impi 3-5$
\end{logicproof}