1. N⊃(∼R⊃C)
2. ∼C
/ ∼R ⊃ ∼N
3. N⊃(~∼R∨C) 1, material implication
4. N⊃(R∨C) 3, double negation
5. ~N∨(R∨C) 4, material implication
6. (~N∨R)∨C 5, assiation
7. C∨(~N∨R) 6, commutation
8. ~N∨R 7,2, disjunctive syllogism
9. R∨~N 8, commutation
10. ~~R∨~N 9, double negation
11. ~R⊃~N 10, material implication
Edwin