\begin{definition}[Definition:Class Intersection/Class of Sets]
Let $\Bbb C$ be a class of sets.
The '''intersection of $\Bbb C$''' is:
:$\ds \bigcap \Bbb C := \set {x: \forall S \in \Bbb C: x \in S}$
That is, the class of all objects that are elements of all the elements of $\Bbb C$.
Thus:
:$\ds \bigcap \set {S, T} := S \cap T$
\end{definition}