Proofs III - Proving Theorems
Prove: (C ⊃ D) ≡ (~C v D)
| 1. | (C ⊃ D) | assump | cp | sp1 |
| 2. | (~C v D) | CE | 1 | sp1 |
| 3. | (C ⊃ D) ⊃ (~C v D) | cp | 1,2 | |
| 4. | (~C v D) | assump | cp | sp2 |
| 5. | (C ⊃ D) | CD | 4 | sp2 |
| 6. | (~C v D) ⊃ (C ⊃ D) | cp | 4,5 | |
| 7. | ((C ⊃ D) ⊃ (~C v D)) & ((~C v D) ⊃ (C ⊃ D)) | conj | 3,6 | |
| 8. |
(C ⊃ D) ≡ (~C v D) |
BE | 7 |