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) | $\bigcup_{j \in J} E_j$ is the D77: Set union of $E = \{ E_j \}_{j \in J}$ |
Then
(1) | \begin{equation} \forall \, i \in J : E_i \subseteq \bigcup_{j \in J} E_j \end{equation} |
(2) | \begin{equation} \forall \, j \in J : E_j \subseteq X \quad \implies \quad \bigcup_{j \in J} E_j \subseteq X \end{equation} |