If $\cap_{j=1}^{n}I_{j} \subseteq P$ for any ideals $I_1,I_2,..I_n$, then $I_j \subseteq P$ for some $j$ $P$ is a prime ideal if $P$ satisfies the following : If $\bigcap\limits_{j=1}^{n}I_{j}  \subseteq P$ for any ideals $I_1,I_2,..I_n$, then $I_j \subseteq P$ for some $j$, where $R$ is a commutative ring with unity:
I started off with let $xy \in P$, for $x$,$y \in R$. I need to create ideals such that whose intersection is precisely $xy$. I could think of $(x)$ and $(y)$ but I cann't guarantee that their intersection is precisely $xy$
Any hint on how to proceed

When it's hard to get a grip on the logic of a problem, try the contrapositive.  Suppose that $I_j\not\subset P$ for all $j$, so there are some $a_j \in I_j$ with $a_j \notin P$.  And we are very nearly done.
