| Number | Statement | Lines Used | Reason |
| 1 | ~N -> [ (B -> D) -> (N v ~E) ] | ||
| 2 | (B -> E) -> ~N | ||
| 3 | B -> D | ||
| 4 | D -> E | ||
| :. | ~D | ||
| 5 | B -> E | 3,4 | Hypothetical Syllogism |
| 6 | ~N | 2,5 | Modus Ponens |
| 7 | (B -> D) -> (N v ~E) | 1,6 | Modus Ponens |
| 8 | N v ~E | 7,3 | Modus Ponens |
| 9 | ~E | 8,6 | Disjunctive Syllogism |
| 10 | ~D | 4,9 | Modus Tollens |