reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds (a '&' b)=I_el(Y)
  implies (a 'or' b)=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  assume
A1: (a '&' b)=I_el(Y);
  for x being Element of Y holds (a 'or' b).x=TRUE
  proof
    let x be Element of Y;
    (a '&' b).x= TRUE by A1,BVFUNC_1:def 11;
    then
A2: a.x '&' b.x=TRUE by MARGREL1:def 20;
    then a.x=TRUE by MARGREL1:12;
    then (a 'or' b).x =TRUE 'or' TRUE by A2,BVFUNC_1:def 4
      .=TRUE;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
