Let $X$ be a D11: Set.
Let $E_j$ be a D11: Set for each $j \in J$ such that
Let $E_j$ be a D11: Set for each $j \in J$ such that
(i) | $\bigcap_{j \in J} E_j$ is the D76: Set intersection of $E = \{ E_j \}_{j \in J}$ |
Then
\begin{equation}
X \subseteq \bigcap_{j \in J} E_j
\quad \iff \quad \forall \, j \in J : X \subseteq E_j
\end{equation}