reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds (a '&' 'not' a) 'imp'
  b=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  for x being Element of Y holds ((a '&' 'not' a) 'imp' b).x=TRUE
  proof
    let x be Element of Y;
    ((a '&' 'not' a) 'imp' b).x ='not' (a '&' 'not' a).x 'or' b.x by
BVFUNC_1:def 8
      .='not'( a.x '&' ('not' a).x) 'or' b.x by MARGREL1:def 20
      .=('not' a.x 'or' 'not' 'not' a.x) 'or' b.x by MARGREL1:def 19
      .=TRUE 'or' b.x by XBOOLEAN:102
      .=TRUE;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
