Conditinal probability theorem

I have to either prove or disprove the following:

If , then (Assuming )

After trying to prove this generally a million times and failing, I decided to find a counter example, I'm not sure if this works though.

All the following events have to do with rolling one fair dice.

A is getting a "2"

B is getting an odd number

C is getting an even number

Now

i.e.

but I believe that

i.e

and (i.e

So this contradicts the hypothesis, but I am not sure if I calculated the probabilities of and right.

Thank you for your help.