Start out assuming the negation of the conclusion and reach a contradiction.
The conclusion is ~A, so its negation is ~~A

A contradiction is always in the form p & ~p. It's C & ~C.  We reach it in step
10.

1. (A & B) ⊃C
2. B & ~C/~A

          | 3. ~~A       Assumption for Indirect Proof
          | 4. A         3, Double Negation
          | 5. B         2, Simplification
          | 6. A & B     4,5, Conjunction     
          | 7. C         1,6, Modus Ponens
          | 8. ~C & B    2, Commutation
          | 9. ~C        8, Simplification
          |10. C & ~C   7,9, Conjunction  
          
11. ~A     Lines 3-10 for Indirect Proof

Edwin