reserve Y for non empty set;

theorem Th25:
  for a being Function of Y,BOOLEAN holds I_el Y 'imp' (I_el
  Y 'imp' a)=I_el Y implies a=I_el Y
proof
  let a be Function of Y,BOOLEAN;
  assume I_el Y 'imp' (I_el Y 'imp' a)=I_el(Y);
  then I_el Y 'imp' a=I_el(Y) by Th2;
  hence thesis by Th2;
end;
