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   \begin{tabular}{r l l}
      1 & $P\wedge \neg P$ & Pr \\ 
      2 & $P$   &1 \\ 
      3 & $(P\wedge \neg P)\to P$ & 1,2,CP \\ 
      4 & $\neg P$ & 1 \\
      5 & $\neg (P\wedge \neg P)$& 3,4, MT\\ 
      6 & $\neg P \vee \neg\neg P$ & 5\\
      7 & $\neg P \to \neg P$ & ``Added" rule\\
      8 & $\neg\neg P \to P$ &Double negation\\
      9 & $\neg P \vee  P$  &6,7,8\\
     10 & $P\vee \neg P$ & 9
    \end{tabular} 


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