ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4270 on D77: Set union
Set union with empty set
Formulation 0
Let $\emptyset$ be the D13: Empty set.
Let $X_j$ be a D11: Set for each $j \in J$ such that
(i) \begin{equation} J \neq \emptyset \end{equation}
(ii) \begin{equation} X_{j_0} = \emptyset \end{equation}
Then \begin{equation} \bigcup_{j \in J} X_j = \bigcup_{j \in J \setminus \{ j_0 \}} X_j \end{equation}