\begin{definition}[Definition:Class Intersection]
Let $A$ and $B$ be two classes.
The '''(class) intersection''' $A \cap B$ of $A$ and $B$ is defined as the class of all sets $x$ such that $x \in A$ and $x \in B$:
:$x \in A \cap B \iff x \in A \land x \in A$
or:
:$A \cap B = \set {x: x \in A \land x \in B}$
\end{definition}