Quotient Structure is Well-Defined

Theorem
Let $\struct {S, \circ}$ be an algebraic structure.

Let $\RR$ be a congruence relation on $\struct {S, \circ}$.

Let $S / \RR$ be the quotient set of $S$ by $\RR$.

Let $\circ_\RR$ be the operation induced on $S / \RR$ by $\circ$.

Then $\circ_\RR$ is a well-defined operation in the quotient structure $\struct {S / \RR, \circ_\RR}$.