reserve B,C,D for Category;

theorem Th18:
  for a being Object of C holds (id a) opp = id(a opp)
 proof let a be Object of C;
  for b being Object of C opp holds
     (Hom(a opp,b) <> {} implies
       for f being Morphism of a opp,b holds f(*)((id a) opp) = f)
   & (Hom(b,a opp) <> {} implies
     for f being Morphism of b,a opp holds ((id a) opp)(*)f = f)
        by Lm1;
  hence (id a) opp = id(a opp) by CAT_1:def 12;
 end;
