Greatest Common Divisor is at least 1

Theorem
The greatest common divisor is at least $1$:


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

Proof
From One Divides all Integers:
 * $\forall a, b \in \Z_{\ne 0}: 1 \mathop \backslash a \land 1 \mathop \backslash b \implies 1 \le \gcd \left\{{a, b}\right\}$