Inference Rules for Propositional Logic

1. Modus Ponens or Implication-Elimination:

   A => B, A
   ---------
       B
   

2. And-Elimination:

   A1 and A2 and ... An
   --------------------
           Ai
   

3. And-Introduction:

     A1, A2, ... An
   --------------------
   A1 and A2 and ... An
   

4. Or-Introduction:

          Ai
   ------------------
   A1 or A2 or ... An
   

5. Double-Negation Elimination:

   NOT(NOT(A))
   -----------
        A
   

6. Unit Resolution:

   A or B, NOT(B)
   ---------------
           A
   

7. Resolution:

   A or B, NOT(B) or C
   -------------------
           A or C