I am recently studying modern algebra and came across this question in my textbook. This conclusion was used directly without any proof. I just wonder why it is true.

I first searched math.stackexchange for something related to intersections of two Sylow-P subgroups and didn't get any strong statements.

Here's the question:

Proof : $ P' \cap N(P) = P' \cap P $, P' and P are Sylow-P sub-groups and N(P) is the normaliser of P.

Thanks in advance!