Solutions to Easy Proofs in QL
Proof 4
| 1. | (∃x)[(Ax ≡ (Bx v ~Cx)] | premise | |
| 2. | (∃x)Cx ⊃ (x)Ax | premise | |
| 3. | (x)~Bx & (x)Ax | premise | |
| 4. | (x)Ax | simp, 3 | |
| 5. | (x)~Bx | simp. 3 | |
| 6. | Aa ≡ (Ba v ~Ca) | E.I., 1, flag a | |
| 7. | ((Aa ⊃ (Ba v ~Ca)) & ((Ba v ~Ca)⊃ Aa) | B.E. 6 | |
| 8. | (Aa ⊃ (Ba v ~Ca)) | simp. 7 | |
| 9. | Aa | U.I. 4 | |
| 10. | (Ba v ~Ca) | M.P. 8, 9 | |
| 11. | ~Ba | U.I. 5 | |
| 12. | ~Ca | D.S. 10, 11 | |
| 13. | (∃x)~Cx | E.I. 12 | |
| 14. | ~(x)Cx | Q.N. 13 |