underbound belongs to ideal of lattice

Question

Let $(L,\leq)$ be a complete lattice and suppose $A$ is an ideal of $L$ (i.e. for all $i \in I$ and $a \in L$, one has that $a \wedge i \in I$). Suppose $c \in L$ is such that $c \leq \bigvee A'$, where $A' \subseteq A$ is a finite subset of $A$. How does one show that $c \in A$? If one has that $\bigvee A' \in A$, then this is of course obvious, but I am not sure if this holds or not.