Let $E_1, \, \ldots, \, E_N$ each be a D11: Set such that

(i) | $\bigcap_{n = 1}^N E_n$ is a D76: Set intersection for $E_1, \, \ldots, \, E_N$ |

Then
\begin{equation}
\bigcap_{n = 1}^N E_n
\subseteq E_1, \quad
\bigcap_{n = 1}^N E_n
\subseteq E_2, \quad
\ldots, \quad
\bigcap_{n = 1}^N E_n
\subseteq E_N
\end{equation}