reserve B,C,D for Category;

theorem
  for a,b being Object of C st Hom(a,b)<>{}
  for f being Morphism of a,b holds f opp opp = f
 proof let a,b be Object of C;
  assume
A1: Hom(a,b)<>{};
  then
A2: Hom(b opp,a opp)<>{} by Th4;
  let f be Morphism of a,b;
  thus f opp opp = f opp by A2,Def6
     .= f by A1,Def6;
 end;
