reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds (a '&' b) 'imp' b=I_el (Y)
proof
  let a,b be Function of Y,BOOLEAN;
  for x being Element of Y holds ((a '&' b) 'imp' b).x=TRUE
  proof
    let x be Element of Y;
    ((a '&' b) 'imp' b).x ='not' (a '&' b).x 'or' b.x by BVFUNC_1:def 8
      .=('not' a.x 'or' 'not' b.x) 'or' b.x by MARGREL1:def 20
      .='not' a.x 'or' ('not' b.x 'or' b.x)
      .='not' a.x 'or' TRUE by XBOOLEAN:102
      .=TRUE;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
