# Complete problems in NP∩coNP

I often read in Complexity literature that NP∩coNP is unlikely to have any complete problems. Is that unlikelihood "proved" ?

By proved, I mean that there would be a theorem that would relate the existence of such a problem to, by instance, the collapse of PH, or any other equality that is strongly believed not to hold (and that at least would be a major breakthrough).

• – Yuval Filmus Jan 20 '18 at 16:00