reserve Y for non empty set;

theorem Th2:
  for b being Function of Y,BOOLEAN st (I_el(Y) 'imp' b)=I_el
  (Y) holds b=I_el(Y)
proof
  set a=I_el(Y);
  let b be Function of Y,BOOLEAN;
  assume
A1: a 'imp' b=I_el(Y);
  for x being Element of Y holds b.x=TRUE
  proof
    let x be Element of Y;
    (a 'imp' b).x=TRUE by A1,BVFUNC_1:def 11;
    then a.x=TRUE & ('not' a.x) 'or' b.x=TRUE by BVFUNC_1:def 8,def 11;
    then FALSE 'or' b.x=TRUE by MARGREL1:11;
    hence thesis by BINARITH:3;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
