is an order isomorphism between X and Y also an order embedding from X into Y?

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is an order isomorphism between X and Y also an order embedding from X into Y?

Please assume that X and Y are both well-ordered sets.

I think the answer is yes.. but am not 100% sure. Thanks in advance for any tips or guidance you can provide.

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By definition, an embedding is an injective homomorphism, so any isomorphism would qualify.