theorem Th69:
  not Collinear a,b,c implies Plane(a,b,c) is_plane & a in Plane(a,b,c) &
  b in Plane(a,b,c) & c in Plane(a,b,c) & (for u,v being POINT of S st
  u in Plane(a,b,c) & v in Plane(a,b,c) & u <> v holds
  Line(u,v) c= Plane(a,b,c))
  proof
    assume not Collinear a,b,c;
    then ex E be Subset of S st Plane(a,b,c) = E & E is_plane & a in E &
      b in E & c in E by Th49;
    hence thesis by Th46;
  end;
