Order Isomorphism is Reflexive

Theorem
Let $\struct {S, \preccurlyeq}$ be an ordered set.

Then $\struct {S, \preccurlyeq}$ is isomorphic to itself.

Proof
Let $I_S: S \to S$ denote the identity mapping on $S$.

From Identity Mapping is Order Isomorphism, $I_S: \struct {S, \preccurlyeq} \to \struct {S, \preccurlyeq}$ is an order isomorphism.

The result follows.