Quotient Ring of Commutative Ring is Commutative

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

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

Let $\struct {R / J, +, \circ}$ be the quotient ring defined by $J$.

If $\struct {R, +, \circ}$ is a commutative ring, then so is $\struct {R / J, +, \circ}$.

Proof
Let $\struct {R, +, \circ}$ be a commutative ring

That means $\circ$ is commutative on $R$.

Thus: