# Order Isomorphism is Equivalence Relation/Proof 2

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## Theorem

Order isomorphism between ordered sets is an equivalence relation.

So any given family of ordered sets can be partitioned into disjoint classes of isomorphic sets.

## Proof

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

The result follows directly from Relation Isomorphism is Equivalence Relation.

$\blacksquare$