reserve Y for non empty set;
reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds (a 'imp' b) '&' 'not'
  b = 'not' a '&' 'not' b
proof
  let a,b be Function of Y,BOOLEAN;
    let x be Element of Y;
    ((a 'imp' b) '&' 'not' b).x =(a 'imp' b).x '&' ('not' b).x by
MARGREL1:def 20
      .=('not' b).x '&' ('not' a.x 'or' b.x) by BVFUNC_1:def 8
      .=(('not' b).x '&' 'not' a.x) 'or' (('not' b).x '&' b.x) by
XBOOLEAN:8
      .=(('not' b).x '&' 'not' a.x) 'or' (b.x '&' 'not' b.x) by
MARGREL1:def 19
      .=(('not' b).x '&' 'not' a.x) 'or' FALSE by XBOOLEAN:138
      .=('not' b).x '&' 'not' a.x
      .=('not' b).x '&' ('not' a).x by MARGREL1:def 19
      .=('not' a '&' 'not' b).x by MARGREL1:def 20;
    hence thesis;
end;
