Nine convex sets determine a pentagon with convex sets as vertices

It is proved that if ℱ is a family of nine pairwise disjoint compact convex sets in the plane such that no member of ℱ is contained in the convex hull of the union of two other sets of ℱ, then ℱ has a subfamily ℱ′ with five elements such that no member of ℱ′ is contained in the convex hull of the union of the other sets of ℱ′.