reserve Y for non empty set;

theorem ::De'Morgan
  for a,b,c being Function of Y,BOOLEAN holds 'not' (a '&' b '&' c
  )=('not' a) 'or' ('not' b) 'or' ('not' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
  'not' (a '&' b '&' c) ='not' (a '&' b) 'or' ('not' c) by BVFUNC_1:14
    .=('not' a) 'or' ('not' b) 'or' ('not' c) by BVFUNC_1:14;
  hence thesis;
end;
