$\forall$$m$, $a$, ${\it a'}$, $b$, ${\it b'}$:$\mathbb{Z}$. ($a$ = ${\it a'}$ mod $m$) $\Rightarrow$ ($b$ = ${\it b'}$ mod $m$) $\Rightarrow$ (($a$+$b$) = (${\it a'}$+${\it b'}$) mod $m$)