
theorem Th22:
  for C1,C2 being Category, F being Functor of C1,C2 for a being
  Object of C1 holds (Psi F).idsym(a) = idsym(F.a)
proof
  let C1,C2 be Category, F be Functor of C1,C2;
  let a be Object of C1;
A1: dom Obj F = the carrier of C1 by FUNCT_2:def 1;
  (idsym a)`1 = 1 & (idsym a)`2 = <*a*>;
  hence (Psi F).idsym(a) = [1,(Obj F)*<*a*>] by Def12
    .= [1,<*(Obj F).a*>] by A1,Lm4
    .= idsym(F.a);
end;
