And with "păcat" having a negative meaning, that makes four of them :)
Levity aside, yes, double negatives are always used like this. The two negatives (NIMENI + NU) don't make a positive. It is incorrect to skip the negation "nu". "fără" has nothing to do with this.
Here are more examples so you get used to double negatives:
NICIUN copil NU cântă acum. = No child is singing now.
NIMIC NU-mi place. = I like nothing. / I don't like anything.
NU merg NICĂIERI. = I go nowhere. / I don't go anywhere.
În deșert NU plouă NICIODATĂ. = It never rains in the desert.