I have found the following statement:
Let $R$ be a Noetherian ring and $x$ is a non-zero divisor of $R$. Let $P$ be a prime ideal associated to $xR$. Then by Prime Avoidance there exists a non-zero divisor $y\in R$ such that $P=xR:_R y \,\,\,\,( xR:_R y:=\{a\in R;ay\in xR\}).$
Can someone please explain how we get such $y$ from Prime Avoidance.