# Principal Ideal Avoidance [duplicate]

Let $$R$$ be a commutative ring with unit. Is it true that given an ideal $$I$$ and $$r \geq 2$$ principal ideals $$P_1, ..., P_r$$, then if $$I \subseteq \bigcup_{i = 1}^r P_i$$, $$I \subseteq P_i$$ for some $$i$$? This would be the analogous of the Prime Avoidance Lemma for principal ideals.