# Identity Mapping is Order Isomorphism/Proof 2

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## Theorem

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

The identity mapping $I_S$ is an order isomorphism from $\struct {S, \preceq}$ to itself.

## Proof

An ordered set is a relational structure where order isomorphism is a special case of relation isomorphism.

The result follows directly from Identity Mapping is Relation Isomorphism.

$\blacksquare$