Let $X$ be a D11: Set.
Let $E_j$ be a D11: Set for each $j \in J$.

Then \begin{equation} \forall \, j \in J : E_j \in \mathcal{P}(X) \quad \implies \quad \bigcap_{j \in J} E_j \in \mathcal{P}(X) \end{equation}