reserve B,C,D for Category;

theorem
  for S being Contravariant_Functor of C,B, c being Object of C holds (
  Obj *'S).(c opp) = (Obj S).c
proof
  let S be Contravariant_Functor of C,B, c be Object of C;
  thus (Obj *'S).(c opp) = (Obj S).(opp (c opp)) by Th41
    .= (Obj S).c;
end;
