Greatest Common Divisor is at least 1

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


 * $$\forall a, b \in \Z^*: \gcd \left\{{a, b}\right\} \ge 1$$

Proof
$$\forall a, b \in \Z^*: 1 \backslash a \land 1 \backslash b \Longrightarrow 1 \le \gcd \left\{{a, b}\right\}$$.