Proof of Fundamental Theorem of Poker?

[de Moivre]

Sklansky's Fundamental Theorem of Poker says essentially that it is optimal to play your hand in the way you would play it if you could see your opponents' cards. It is said to apply always in heads up play and usually with more than two players.

Can anyone supply a proof or refer me to one in the poker or game theory literature? (There is no proof given in my 1994 edition of The Theory of Poker.)

Actually, I suspect it is a general result in game theory, which is not limited to poker. If so, I would like a precise formulation and a proof. Thanks in advance for any leads.