Proximal compact spaces are Corson compact

J. Bell defined a topological space X to be proximal if X has a compatible uniformity with respect to which the first player has a winning strategy in a certain ω-length game. As noted by P.J. Nyikos, it follows easily from Bell's results that Corson compact spaces are proximal. We answer a question of Nyikos by showing that a compact space is proximal iff it is Corson compact.