reserve B,C,D for Category;

theorem
  for F being Contravariant_Functor of C,D, c being Object of C holds (
  Obj *'F*').(c opp) = ((Obj F).c) opp
proof
  let F be Contravariant_Functor of C,D, c be Object of C;
  *'F is Functor of C opp,D by Th53;
  hence (Obj *'F*').(c opp) = ((Obj *'F).(c opp)) opp by Th40
    .= ((Obj F).(opp(c opp))) opp by Th41
    .= ((Obj F).c) opp;
end;
