ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4265 on D76: Set intersection
Finite set intersection with empty set is empty
Formulation 0
Let $\emptyset$ be the D13: Empty set.
Let $X_1, \ldots, X_N$ each be a D11: Set such that
(i) \begin{equation} \exists \, n \in 1, \ldots, N : X_n = \emptyset \end{equation}
Then \begin{equation} \bigcap_{n = 1}^N X_n = \emptyset \end{equation}