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) | \begin{equation} J \neq \emptyset \end{equation} |
(ii) | $\bigcap_{j \in J} E_j$ is the D76: Set intersection of $E = \{ E_j \}_{j \in J}$ |
Then
(1) | \begin{equation} \forall \, i \in J : \bigcap_{j \in J} E_j \subseteq E_i \end{equation} |
(2) | \begin{equation} \forall \, j \in J : X \subseteq E_j \quad \implies \quad X \subseteq \bigcap_{j \in J} E_j \end{equation} |