연습문제 V
게시글 주소: https://orbi.kr/00078657833
1. (∃x)Bx → (∀x)(Dx → Ax)
2. (∃x)Dx → (∀x)(Ax → Cx) /(∃x)Bx → (∀x)(Dx → Cx)
3. ~{(∃x)Bx → (∀x)(Dx → Cx)} A
4. ~{~(∃x)Bx ⋁ (∀x)(Dx → Cx)} 3, Impl.
5. ~~(∃x)Bx ⋀ ~(∀x)(Dx → Cx) 4, DM
6. (∃x)Bx ⋀ ~(∀x)(Dx → Cx) 5, DN
13. Da 14. (∃x)Dx 15. (∀x)(Ax → Cx) 16. (∃x)Bx 17. (∀x)(Dx → Ax) 18. Da → Aa 12, DN
13, ∃I
2, 14, MP
6, Simp.
2, 16, MP
17, ∀E
7. ~(∀x)(Dx → Cx) 8. (∃x)~(Dx → Cx) 9. ~(Da → Ca) 10. ~(~Da ⋁ Ca) 11. ~~Da ⋀ ~Ca 12. ~~Da 6, Simp.
7, QN
8, ∃E
9, Impl.
10, DM
11, Simp.
19. Aa → Ca 20. Da → Ca 21. Ca 15, ∀E
18, 19, HS
13, 20, MP
22. ~Ca 23. Ca ⋀ ~Ca 11, Simp.
21, 22, Conj.
24. (∃x)Bx → (∀x)(Dx → Cx) 3-23, IP
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