reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds a 'imp' (b 'imp' (a
  '&' b))=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  for x being Element of Y holds (a 'imp' (b 'imp' (a '&' b))).x=TRUE
  proof
    let x be Element of Y;
    (a 'imp' (b 'imp' (a '&' b))).x ='not' a.x 'or' (b 'imp' (a '&' b)).
    x by BVFUNC_1:def 8
      .='not' a.x 'or' ('not' b.x 'or' (a '&' b).x) by BVFUNC_1:def 8
      .='not' a.x 'or' ('not' b.x 'or' (a.x '&' b.x)) by
MARGREL1:def 20
      .='not' a.x 'or' (('not' b.x 'or' a.x) '&' ('not' b.x 'or' (b)
    .x)) by XBOOLEAN:9
      .='not' a.x 'or' (TRUE '&' ('not' b.x 'or' a.x)) by XBOOLEAN:102
      .=('not' a.x 'or' a.x) 'or' 'not' b.x
      .=TRUE 'or' 'not' b.x by XBOOLEAN:102
      .=TRUE;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
