reserve A,B,C for Category,
  F,F1,F2,F3 for Functor of A,B,
  G for Functor of B, C;
reserve m,o for set;

theorem Th16:
  for a being Object of A holds id F.a = id(F.a)
proof
  let a be Object of A;
  thus id F.a = (id F qua Function of the carrier of A, the carrier' of B).a
  by Def4
    .= id (F.a) by Def3;
end;
