Definition:Epsilon Relation

Definition
As $\in$ is technically not a class itself nor a relation, but a primitive, it is necessary to introduce a class which behaves identically to the membership relation $\in$ for sets. This will be referred to as the epsilon relation and will be denoted by $E$.


 * $E = \{ ( x, y ) : x \in y \}$

The relation is a collection of ordered pairs such that $( x, y ) \in E \iff x \in y$. (Notice that this does not hold for proper classes).