Antireflexive Relation/Examples/Distinctness

Example of Antireflexive Relation
Let $S$ be a set.

Let $\RR$ be the relation on $S$ defined as:
 * $\forall x, y \in S: x \mathrel \RR y$ $x$ is distinct from $y$

Then $\RR$ is antireflexive.

Proof
No element of $S$ is distinct from itself.

Hence the result by definition of distinct.