Prime avoidance

If an ideal $I$ is contained in a finite union of prime ideals ${\mathfrak{p}}_1\cup \cdots \cup {\mathfrak{p}}_r$, then $I$ is contained in one of the ${\mathfrak{p}}_i$. Equivalently, if none of the primes contains $I$, one can choose an element of $I$ outside all of them.