This is theorem 4.4 from
D. Quillen, The Spectrum of an Equivariant Cohomology Ring I, Annals of Mathematics 94, 549–572 (1971).
An earlier (unpublished) reference, cited here is
M.F. Atiyah and G. Segal, Equivariant cohomology and localization, lecture notes, 1965, Warwick.