Diagonal_Relation_is_Ordering_and_Equivalence

Let $\left({S, \Delta_S}\right)$ be a relational structure where $\Delta_S$ is the diagonal relation, defined as $\forall x, y \in S: \paren {x, y} \in \Delta_S \iff x = y$ Then $\Delta_S$ is the '''only''' relation on $S$ which is both an equivalence and an ordering.