Definition:Epsilon Relation/Restriction

Let $S$ be a set.
The restriction of the epsilon relation on $S$ is defined as the endorelation $\Epsilon {\restriction_S} = \left({S, S, \in_S}\right)$, where:
$\in_S \; := \left\{{\left({x, y}\right) \in S \times S: x \in y}\right\}$