
theorem Th2:
  for C being Category, D,E being Categorial Category for F being
  Functor of C,D for G being Functor of C,E st F = G holds Obj F = Obj G
proof
  let C be Category, D,E be Categorial Category;
  let F be Functor of C,D;
  let G be Functor of C,E such that
A1: F = G;
A2: now
    let x be object;
    assume x in the carrier of C;
    then reconsider a = x as Object of C;
A3: a = dom id a;
    hence (Obj F).x = dom (F.(id a qua Morphism of C)) by CAT_1:69
      .= (F.(id a qua Morphism of C))`11 by CAT_5:13
      .= dom (G.(id a qua Morphism of C)) by A1,CAT_5:13
      .= (Obj G).x by A3,CAT_1:69;
  end;
  thus thesis by A2;
end;
