Let $G$ be a finite group, $H$ and $K$ subgroups of $G$ such that $G=HK$. Show that there exists a $p$-Sylow subgroup $P$ of G such that $P=(P\cap H)(P\cap K)$.
I looked at the proof here, but I can't understand step "(3) It is clear in this situation that $P=(P\cap H)(P\cap K)$." Help.