Integers Modulo m under Addition form Abelian Group

Theorem
Let $\Z_m$ is the set of integers modulo $m$

Let $+_m$ be the operation of addition modulo $m$.

Then the structure $\left({\Z_m, +_m}\right)$ is an abelian group.

Proof
From Integers Modulo m under Addition form Cyclic Group, $\left({\Z_m, +_m}\right)$ is a cyclic group.

The result follows from Cyclic Group is Abelian.