Let A, B, C be events.

Show that if P(A|B) = 1, then P(Bc|Ac) = 1

Bc= B complement, Ac = A complement.

I got:

P(A|B) = P(A and B)/ P(B)

1= P(A)/P(B) because P(A|B)=1
1-P(A) = 1-P(B)
P(Ac) = P(Bc)
P(Bc)/P(Ac) = 1 and this is only true if P(Bc|Ac) = 1

Is this right?