Coprimality Relation is Symmetric

Theorem
Consider the coprimality relation on the set of integers:
 * $\forall x, y \in \Z: x \perp y \iff \gcd \set {x, y} = 1$

where $\gcd \set {x, y}$ denotes the greatest common divisor of $x$ and $y$.

Then:
 * $\perp$ is symmetric.

Proof
Hence the result by definition of symmetric relation.