2nd law of thermodynamics: equivalency of statements

Clausius statement (according to Wikipedia):

No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

Clausius equality:

$$\oint \frac{\delta Q}{\theta} = 0$$ (which implies existence of entropy $S$: $dS = \frac{\delta Q}{\theta}$)

They both are the statements of the second law of thermodynamics. How to prove their equivalence? This prove seems to be frequently omitted from books, I don't know why.

Frankly speaking, Clausius statement may be easily derived from Clausius equality. The question is derivation of the equality from the statement.

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As reference: "Huang K. Statistical Mechanics", page 14,15. Basically the integral is obtained as a limit of a sum of recycled energy contributions represented by heat flows between different temperatures, which work according to the second law. – Nick Kidman Jan 2 '12 at 14:06