Order Isomorphism is Equivalence Relation/Proof 1

Theorem
Order isomorphism between posets is an equivalence relation.

Proof

 * Reflexive:

Follows directly from the fact that the identity mapping is an order isomorphism.


 * Symmetric:

Follows directly from the fact that the inverse of an order isomorphism is itself an order isomorphism.


 * Transitive:

Follows directly from the fact that the composite of two order isomorphisms is itself an order isomorphism.