Given the events $A, B$ the conditional probability of $A$ supposing that $B$ happened is:

$$P(A | B)=\frac{P(A\cap B )}{P(B)}$$

Can we write that for the Events $A,B,C$, the following is true?

$$P(A | B\cap C)=\frac{P(A\cap B\cap C )}{P(B\cap C)}$$

I have couple of problems with the equation above; it doesn't always fit my logical solutions.

If it's not true, I'll be happy to hear why.

Thank you.