reserve Y for non empty set;

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