reserve B,C,D for Category;

theorem Th13:
 for a,b being Object of C opp,f being Morphism of a,b st Hom(a,b) <> {}
  holds opp f is Morphism of opp b,opp a
proof
  let a,b be Object of C opp, f be Morphism of a,b;
  assume Hom(a,b) <> {};
  then f in Hom(a,b) by CAT_1:def 5;
  then opp f in Hom(opp b,opp a) by Th5;
  hence thesis by CAT_1:def 5;
end;
