reserve B,C,D for Category;

theorem
  for a,b,c being Object of C, f being Morphism of a,b, g being Morphism
  of b, c st Hom(a,b) <> {} & Hom(b,c) <> {}
    holds (g*f) opp = (f opp)(*)(g opp)
proof
  let a,b,c be Object of C, f be Morphism of a,b, g be Morphism of b,c;
  assume
A1: Hom(a,b) <> {} & Hom(b,c) <> {};
A2: Hom(a,c) <> {} by A1,CAT_1:24;
  thus (g*f) opp = g*f by A2,Def6 .= (g(*)f) opp by A1,CAT_1:def 13
    .= (f opp)(*)(g opp) by A1,Th14;
end;
