reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;

theorem Th1:
  'not' (a 'imp' b) = a '&' 'not' b
proof
  thus 'not' (a 'imp' b)='not' ('not' a 'or' b) by BVFUNC_4:8
    .='not' 'not' a '&' 'not' b by BVFUNC_1:13
    .=a '&' 'not' b;
end;
