Bases in Vector Spaces and the Axiom of Choice
James D. Halpern · Proceedings of the American Mathematical Society · 1966
Fx= \f:XEDf), all XG Y.I is proper by Philip Hall's theorem.Let J be an ultrafilter including I. Then for each j£F there is a unique »G-X such that \f:f{X) =x\EJ-This correspondence defines the required function.