ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4264 on D326: Cartesian product
Cartesian product with empty set is empty
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} \exists \, j \in J : X_j = \emptyset \end{equation}
Then \begin{equation} \prod_{j \in J} X_j = \emptyset \end{equation}