\begin{logicproof}{1}
p \imp q  & \prem \\
\neg p \vee p   & $\LEM$ \\
    \begin{subproof}
        \neg p & \assum \\
        \neg p \lor q & $\ori{1} 3$
    \end{subproof}
    \begin{subproof}
       p & \assum \\
       q & $\imp$e 1,5 \\
       \neg p \lor q & $\ori{2} 6$
    \end{subproof}
 \neg p \lor q & $\ore 2,3-5,5-7$
  \end{logicproof}
