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 $1$:


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

Proof
From One Divides all Integers:
 * $\forall a, b \in \Z: 1 \divides a \land 1 \divides b$

and so:
 * $1 \le \gcd \set {a, b}$

as required.