Greatest Common Divisor is at least 1

Theorem
Let $a, b \in \Z$ be integers.

The greatest common divisor of $a$ and $b$ is at least $1$:


 * $\forall a, b \in \Z_{\ne 0}: \gcd \left\{{a, b}\right\} \ge 1$

Proof
From One Divides all Integers:
 * $\forall a, b \in \Z: 1 \mathrel \backslash a \land 1 \mathrel \backslash b \implies 1 \le \gcd \left\{{a, b}\right\}$