Set of Common Divisors of Integers is not Empty

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

Let $S$ be the set of common divisors of $a$ and $b$.

Then $S$ is not empty.

Proof
From One is Common Divisor of Integers:
 * $1$ is a common divisor of $a$ and $b$.

Thus, whatever $a$ and $b$ are:
 * $1 \in S$

The result follows by definition of empty set.