Equivalence Relation is Congruence iff Compatible with Operation/Proof 2

Theorem
Let $\left({S, \circ}\right)$ be an algebraic structure.

Let $\mathcal R$ be an equivalence relation on $S$.

Then $\mathcal R$ is a congruence relation for $\circ$ iff:

That is, iff $\mathcal R$ is compatible with $\circ$.

Proof
We have that a equivalence relation is a preordering.

Thus the result Preorder Compatible with Operation is Congruence can be applied directly.