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:

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