Probability Theory

[Dirac]

"Hi guys, can someone assist me with this proof?

Suppose X,Y belong to the probability triple (Omega, F, P)

and that E(X|Y)=Y, E(Y|X)=X.

Prove that P(X=Y)=1.

It gives the hint:

Consider E(X-Y;X>c,Y<=c) + E(X-Y;X<=c,Y<=c).

All I can get to is the result

XP(X)-YP(Y)=0

Thanks for any contribution."