Prime Ideal Theorem implies Excluded Middle?

Dear all, does anyone know a reference for the question: Prime Ideal Theorem implies the Excluded Middle ? Certainly, Axiom of Choice implies Excluded Middle, but I have convinced myself that the weaker statement is true and would be grateful for any pointers. Regards, Christopher Townsend PS there are definitely formulations of the PIT that do not use negation. E.g. it is equivalent to the statement that for every Boolean alg. B if x in B has the property that f(x)=0 for every Boolean alg. homomorphism f:B->Omega, then x=0.