Let $X, E_1, \ldots, E_N$ be a D11: Set such that
(i) | $\bigcap_{n = 1}^N E_n$ is the D76: Set intersection of $E_1, \ldots, E_N$ |
Then
\begin{equation}
X \subseteq \bigcap_{n = 1}^N E_n
\quad \iff \quad X \subseteq E_1, \; \ldots, \; X \subseteq E_N
\end{equation}