Quotient Mapping is Surjection

Theorem
Let $S$ be a set.

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

Then the quotient mapping $q_\RR: S \to S / \RR$ is a surjection.

Proof
From Equivalence Class is not Empty, we have that:


 * $\forall \eqclass x \RR \in S / \RR: \exists x \in S: x \in \eqclass x \RR$

and the result follows.