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  1. \begin{logicproof}{2}
  2. \lnot\psi & \prem \\
  3. \varphi \imp \psi & \prem \\
  4. \begin{subproof}
  5. \varphi & \assum \\
  6. \psi & $\impe 1,2$ \\
  7. \bot & $\nege 1,4$
  8. \end{subproof}
  9. \lnot\varphi & $\negi 3-5$
  10. \end{logicproof}