Let $x$ be a D11: Set.
The intersection of $x$ is the D11: Set \begin{equation} \cap x : = \{ z \mid \forall \, y \in x : z \in y \} \end{equation}

Let $X_j$ be a D11: Set for each $j \in J$.
The intersection of $\{ X_j \}_{j \in J}$ is the D11: Set \begin{equation} \bigcap_{j \in J} X_j : = \{ x \mid \forall \, j \in J : x \in X_j \} \end{equation}