Abelianness is quotient-closed

This article gives the statement, and possibly proof, of a group property (i.e., abelian group) satisfying a group metaproperty (i.e., quotient-closed group property)
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Statement

Suppose $G$ is an abelian group and $N$ is a normal subgroup of $G$. Denote by $G/N$ the quotient group. Then, $G/N$ is also an abelian group.

Related facts

• Abelianness is varietal
• Abelianness is subgroup-closed
• Abelian implies every subgroup is normal
• Abelianness is direct product-closed