Diagonal Relation is Equivalence/Examples/Integers

Examples of Use of Diagonal Relation is Equivalence
Let $\Z$ denote the set of integers.

Let $\RR$ denote the relation on $\Z$ defined as:
 * $\forall x, y \in \Z: x \mathrel \RR y \iff x = y$

Then $\RR$ is an equivalence relation such that the equivalence classes are singletons.

Proof
This is an instance of Diagonal Relation is Equivalence.

The result follows from Equivalence Classes of Diagonal Relation.