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}