  By de Vries duality [9], the category ${\sf KHaus}$ of compact Hausdorff
spaces is dually equivalent to the category ${\sf DeV}$ of de Vries algebras.
In [5] an alternate duality for ${\sf KHaus}$ was developed, where de Vries
algebras were replaced by proximity Baer-Specker algebras. The functor
associating with each compact Hausdorff space a proximity Baer-Specker algebra
was described by generalizing the notion of a boolean power of a totally
ordered domain to that of a de Vries power. It follows that ${\sf DeV}$ is
equivalent to the category ${\sf PBSp}$ of proximity Baer-Specker algebras. The
equivalence is obtained by passing through ${\sf KHaus}$, and hence is not
choice-free. In this paper we give a direct algebraic proof of this
equivalence, which is choice-free. To do so, we give an alternate choice-free
description of de Vries powers of a totally ordered domain.
