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