reserve B,C,D for Category;

theorem
  for F being Contravariant_Functor of C,D holds *'F*' is
  Contravariant_Functor of C opp,D opp
proof
  let F be Contravariant_Functor of C,D;
  *'F is Functor of C opp,D by Th53;
  hence thesis by Th56;
end;
