
theorem
  for A, B being category st A, B are_anti-isomorphic holds A, B are_dual
proof
  let A, B be category;
A1: B, B opp are_opposite by Def4;
  assume A, B are_anti-isomorphic;
  then A, B opp are_isomorphic by A1,Th17;
  hence A, B opp are_equivalent by Th5;
end;
