A Map Constant on Equivalence Classes Factors Uniquely through the Quotient

In the setting of Class Theory NBG: the Axioms, Standing Conventions and Basic Notation, let $a$ and $b$ be sets, $R$ an equivalence relation on $a$, $a/R$ the quotient of $a$ by $R$ and $\pi_{R}$ the canonical projection. Let $F:a\to b$ be a map such that, for all $u,v\in a$, if $u\,R\,v$ then the values satisfy $F(u)=F(v)$.

¶ There is exactly one map $G:a/R\to b$ whose composition with $\pi_{R}$ satisfies $G\circ\pi_{R}=F$.