Abelianness is quotient-closed

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