reserve Y for non empty set;

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