reserve B,C,D for Category;

theorem
  for F being Functor of C,D, c being Object of C holds (Obj *'F*').(c
  opp) = ((Obj F).c) opp
proof
  let F be Functor of C,D, c be Object of C;
  *'F is Contravariant_Functor of C opp,D by Th55;
  hence (Obj *'F*').(c opp) = ((Obj *'F).(c opp)) opp by Th43
    .= ((Obj F).(opp (c opp))) opp by Th38
    .= ((Obj F).c) opp;
end;
