Given $R$ and $S$ being number rings corresponding to the number fields $K$ and $L$, such that $K \subset L$, show that $\mathfrak Q \cap R$ is nonzero where $\mathfrak Q$ is any nonzero prime ideal of $S$.
This is from Daniel A. Marcus' Number Fields, Chapter $3$, Theorem $20$. It hints that we can use a norm argument. Please help me.