The Dilworth theorem for finite posets implies that a finite poset contains either a "large" chain or a "large" antichain. I am sure I saw an infinite version of this :


An infinite poset has either an infinite chain or an infinite antichain.


But I can't find a reference to that statement. What is the reference or a proof?



An infinite version of the Dilworth theorem
This is studied in Reverse Mathematics as the [Chain Antichain Principle](https://pdfs.semanticscholar.org/e849/71951a12a859da7d7f46acc78b5374aef557.pdf) (CAC)
and it is observed that it follows from Ramsey's theorem.


