1. N ⊃ (F • A)
2. B ⊃ (R • F) / (N ∨ B) ⊃ (A ∨ R)
|3. N ∨ B Assumption for conditional proof
|4. (F • A) ∨ (R • F) 1,2,3, Constructive dilemma
|5. (F • A) ∨ (F • R) 4, Commutation
|6. F • (A ∨ R) 5, Distribution
|7. (A ∨ R) • F 6, Commutation
|8. A ∨ R 7, Simplification
9. (N ∨ B) ⊃ (A ∨ R) 3-8 Conditional proof.
Edwin