Greatest Common Divisor is at least 1

Theorem
The Greatest Common Divisor is at least $$1$$.

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

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