$\forall$$a$, $b$, ${\it a'}$, ${\it b'}$:$\mathbb{Z}$. ($a$ $\sim$ ${\it a'}$) $\Rightarrow$ ($b$ $\sim$ ${\it b'}$) $\Rightarrow$ (($a$ $\sim$ $b$) $\Leftrightarrow$ (${\it a'}$ $\sim$ ${\it b'}$))