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7272\begin {proof }
7373  \begin {derivation }
74-     1. & $ \Log {K} \Proves  \lnot  !A \lif  (\lnot  !B \lif  \lnot  (!A \lor  !B)$ \Taut  \\ 
74+     1. & $ \Log {K} \Proves  \lnot  !A \lif  (\lnot  !B \lif  \lnot  (!A \lor  !B)) $ \Taut  \\ 
7575    2. & $ \Log {K} \Proves  \Box \lnot  !A \lif 
76-     (\Box \lnot !B \lif  \Box  \lnot  (!A \lor  !B)$   & \RK \\ 
76+     (\Box \lnot !B \lif  \Box  \lnot  (!A \lor  !B)) $   & \RK \\ 
7777    3. & $ \Log {K} \Proves  \Box \lnot  !A \lif  (\lnot  \Box  \lnot  (!A \lor !B)
78-     \lif  \lnot \Box \lnot  !B)) $   & \PL , 2\\ 
78+     \lif  \lnot \Box \lnot  !B)$   & \PL , 2\\ 
7979    4. & $ \Log {K} \Proves  \lnot  \Box  \lnot (!A \lor  !B) \lif  (\Box  \lnot  !A \lif  
8080    \lnot \Box \lnot  !B)$   & \PL , 3\\ 
8181    5. & $ \Log {K} \Proves  \lnot  \Box  \lnot (!A\lor !B) \lif  (\lnot 
 
 
   
 
     
   
   
          
    
    
     
    
      
     
     
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