1.  F -> (P -> N)
2.  ~N * ~~P
/   ~F
-------------------------------------------------------
3.  (F * P) -> N                          1        Exportation
4.  (P * F) -> N                          3        Commutation
5.  P -> (F -> N)                         4        Exportation
6.  ~N * P                                2        Double Negation
7.  P * ~N                                6        Commutation
8.  ~N                                    6        Simplification
9.  P                                     7        Simplification
10. F -> N                                5,9      Modus Ponens
11. ~F                                    10,8     Modus Tollens