The definition of $\displaystyle x \in \cap \mathcal{F}$ is $\displaystyle \forall A (A\in \mathcal{F}\Rightarrow x \in A)$.

Similarly, the definition of $\displaystyle x \in \cap \mathcal{G}$ is $\displaystyle \forall B (B\in \mathcal{G}\Rightarrow x \in B)$.

Could someone please show me how to define $\displaystyle x\in \cap(\mathcal{F} \cup \mathcal{G})$?