Proofs V - Solutions
prove: A ⊃ (B ⊃ E)
| 1. | A ⊃ B | premise | ||
| 2. | B ⊃ ~A | premise | ||
| 3. | A v B | premise | ||
| 4. | A | assump., cp | sp1 | |
| 5. | B | assump., ip | sp1, sp2 | |
| 6. | ~A | mp, | 2, 5 | sp1, sp2 |
| 7. | A & ~A | conju | 4,6 | sp1, sp2 |
| 8. | ~B | i.p. | 5-7 | sp1 |
| 9. | ~B v E | disj | 8 | sp1 |
| 10. | (B ⊃ E) | C.E., | 9 | |
| 11. | A ⊃ (B ⊃ E) | c.p. | 4-9 |