
theorem
  for A, B, C being category st A, B are_dual & B, C are_dual
  holds A, C are_equivalent
proof
  let A, B, C be category such that
A1: A, B opp are_equivalent and
A2: B, C are_dual;
  C, B opp are_equivalent by A2,Def6;
  hence thesis by A1,Th4;
end;
