Let G, X and Y are algebraic schemes over k.(k:field) Assume that G is affine, and that the action is proper. Then f:X -> Y is affine. This is the Proposition0.7 in 'GIT(mumford & Fogarty)' I don't understand the part of the proof of this Prop.

g: G×Y -> X is a proper morphism. P_2: G×Y -> Y is the second projection and affine morphism. and f·g=p_2. The author says "by Chevalley's Theorem(EGA 2, Theorem 6.7.1), f is affine". I can't draw it. Please, help me...

(*Chevalley's Thm: X: affine scheme, Y: noetherian pre-scheme, f: x -> Y is a finite surjective morphism Then Y is also affine.)