Equivalence Class Equivalent Statements/3 iff 6

Theorem
Let $\RR$ be an equivalence relation on $S$.

Let $x, y \in S$.


 * $x \mathrel \RR y$
 * $\eqclass x \RR \cap \eqclass y \RR \ne \O$

Proof
Follows directly from Equivalence Classes are Disjoint.