Definition:Set Intersection/Family of Sets/Two Sets

Definition
Let $I = \left\{{\alpha, \beta}\right\}$ be an indexing set containing exactly two elements.

Let $\left \langle {S_i} \right \rangle_{i \mathop \in I}$ be a family of sets indexed by $I$.

From the definition of the intersection of $S_i$:
 * $\displaystyle \bigcap_{i \mathop \in I} S_i := \left\{{x: \forall i \in I: x \in S_i}\right\}$

it follows that:
 * $\displaystyle \bigcap_{i \mathop \in I} S_i := S_\alpha \cap S_\beta$