Quotient_Epimorphism_is_Epimorphism_Ring

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 $J$. Let $\phi: R \to R / J$ be the quotient (ring) epimorphism from $R$ to $R / J$ $x \in R: \map \phi x = x + J$ Then $\phi$ is a ring epimorphism whose kernel is $J$.