reserve Y for non empty set;

theorem ::De'Morgan
  for a,b,c being Function of Y,BOOLEAN holds 'not' (a 'or' b 'or'
  c)=('not' a) '&' ('not' b) '&' ('not' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
  'not' (a 'or' b 'or' c) ='not' (a 'or' b) '&' ('not' c) by BVFUNC_1:13
    .=('not' a) '&' ('not' b) '&' ('not' c) by BVFUNC_1:13;
  hence thesis;
end;
