Identity Mapping is Ordered Ring Automorphism

Theorem
Let $\left({S, +, \circ, \preceq}\right)$ be an ordered ring.

Then the identity mapping $I_S: S \to S$ is an ordered ring automorphism.

Proof
We have that:
 * an identity mapping is an order isomorphism
 * an identity mapping is a group automorphism
 * an identity mapping is a semigroup automorphism

Hence the result by definition of ordered ring automorphism.