Proofs II, #5
derive (~Q ⊃ ~S)
| 1. | (A v (B & C) | premise | |
| 2. | ((~A ⊃ B) ⊃ D) | premise | |
| 3. | ~D v (S ≡ Q) | premise | |
| 4. | ~(~A ⊃ B) v D | CE | 2 |
| 5. | ~(~~A v B) v D | CE | 4 |
| 6. | ~(A v B) v D | DN | 5 |
| 7. | (A v B) & (A v C) | DIST | 1 |
| 8. | (A v B) | simp | 7 |
| 9. | D | d.s. | 5,8 |
| 10. | (S ≡ Q) | d.s. | 3,9 |
| 11. | (S ⊃ Q) & (Q ⊃ S) | BE | 10 |
| 12. | (S ⊃ Q) | simp | 11 |
| 13. |
(~Q ⊃ ~S) |
CONTRA | 12 |