Divisor Relation is Antisymmetric/Corollary/Proof 1

Corollary to Divides is Antisymmetric
Let $a, b \in \Z$.

If $a \mathop \backslash b$ and $b \mathop \backslash a$ then $a = b$ or $a = -b$.

Proof
Let $a \mathop \backslash b$ and $b \mathop \backslash a$.

Then from Divides is Antisymmetric:
 * $\left\vert{a}\right\vert = \left\vert{b}\right\vert$

The result follows from Every Integer Divides Its Negative and Every Integer Divides Its Absolute Value.