If P[A|B] > P[A|B complement], then show that P[A complement] < P[A complement|B complement].

What I've got so far:

0) P[A intersection B]/P[B] > P[A intersection B complement]/P[B complement]

1) P[A intersection B]*P[B complement] > P[B]*P[A intersection B complement]

2) P[A intersection B] - P[A intersection B]*P[B] > P[B]*P[A] - P[B]*P[A intersection B]

3) P[A intersection B] > P[B]*P[A]

4) P[A] < P[A intersection B]/P[B]

5) P[A] < P[A|B]

6) 1 - P[A complement] < P[A|B]

7) P[A complement] > P[A complement|B]

I'm stuck at this part. Any help would be greatly appreciated.