I've been working on this problem for a while. Could someone show me how to connect the last part?

Let A, B, and C be finite sets. Prove:

If

then A, B, and C must be pairwise disjoint.

Here is what I have:

Suppose A, B, and C are finite sets with .

By inclusion/exclusion, we know that

By cancellation, we have:

I'm just not sure how to connect that to "Thus A, B, and C must be pairwise disjoint."