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