reserve B,C,D for Category;

theorem
  for a,b,c being Object of C
st Hom(b opp,a opp) <> {} & Hom(c opp,b opp) <> {}
  for f be Morphism of a,b, g being Morphism of b,c
  holds (g(*)f) opp = (f opp)(*)(g opp)
proof let a,b,c be Object of C;
 assume Hom(b opp,a opp) <> {} & Hom(c opp,b opp) <> {};
  then Hom(a,b) <> {} & Hom(b,c) <> {} by Th4;
 hence thesis by Th14;
end;
