Direct Proof

(A B) C,     (A ~B) C      \ C

1.         (A B) C                  \ C

2.         (A ~B) C

3.        ~C    ~(A ~B)            2 Transposition

4.        ~C    (~A ~~B)        3 DeMorgan

5.        ~C    (~A B)            4 DN

6.        ~C  (A   B)                5 Implication

7.        ~C    C                          1,6  Hypothetical Syllogism

8.        C   C                            7 Implication

9.        C                                      8 Tautology

 

OK, so there are fewer lines, but did you really see the proof strategy on your own?  Isn't the IP simpler even if longer?