Let be a parameter with parameter space equal to an interval of real numbers (possibly unbounded). Let X have p.d.f. or p.f. fn(x|)

Let θ be a parameter with parameter space Ω equal to an interval of real numbers (possibly unbounded). Let X have p.d.f. or p.f. fn(x|θ) conditional on θ. Let T = r(X) be a statistic. Assume that T is sufficient. Prove that, for every possible prior p.d.f. for θ, the posterior p.d.f. of θ given X = x depends on x only through r(x).