Quotient Ring of Commutative Ring is Commutative

Theorem
Let $\left({R, +, \circ}\right)$ be a ring whose zero is $0_R$ and whose unity is $1_R$.

Let $J$ be an ideal of $R$.

Let $\left({R / J, +, \circ}\right)$ be the quotient ring defined by $J$.

If $\left({R, +, \circ}\right)$ is a commutative ring, then so is $\left({R / J, +, \circ}\right)$.

Proof
If $\left({R, +, \circ}\right)$ is a commutative ring, then that means $\circ$ is commutative on $R$. Thus: