Proofs II, #7
derive B
| 1. | (A ≡ B) ⊃ C | premise | |
| 2. | ~(C v A) | premise | |
| 3. | ~C & ~A | DEM | 2 |
| 4. | ~C | simp | 3 |
| 5. | ~(A ≡ B) | m.t. | 1,4 |
| 6. | ~[(A ⊃ B) & (B ⊃ A)] | BE | 5 |
| 7. | ~[(~A v B) & (B ⊃ A)] | CE | 6 |
| 8. | ~[(~A v B) & (~B v A)] | CE | 7 |
| 9. | ~(~A v B) v ~(~B v A) | DEM | 8 |
| 10. | (~~A & ~B) v ~(~B v A) | DEM | 9 |
| 11. | (~~A & ~B) v (~~B & ~A) | DEM | 10 |
| 12. | (A & ~B) v (~~B & ~A) | DN | 11 |
| 13. | (A & ~B) v (B & ~A) | DN | 12 |
| 14. | ~A | simp | 3 |
| 15. | ~A v B | disj | 14 |
| 16. | ~(A & ~B) | DEM | 15 |
| 17. | (B & ~A) | d.s. | 13,16 |
| 18. | B | simp | 17 |