reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN st ('not' a)=I_el(Y) holds (
  a 'imp' b)=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  assume
A1: 'not' a=I_el(Y);
  for x being Element of Y holds (a 'imp' b).x=TRUE
  proof
    let x be Element of Y;
    ('not' a).x=TRUE by A1,BVFUNC_1:def 11;
    then 'not' a.x=TRUE by MARGREL1:def 19;
    then (a 'imp' b).x =TRUE 'or' b.x by BVFUNC_1:def 8
      .=TRUE by BINARITH:10;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
