Question 1210176
```
1.  (∃x)Ax ⊃ [(∃x)Bx ∨ (x)Cx]         Premise
2.  (∃x)(Ax ⦁ ~Cx)                 Premise
3.  ~(x)Cx ⊃ [(x)Fx ⊃ (x)~Bx]        Premise
4.  Ax ⦁ ~Cx                         EI 2
5.  Ax                                Simp 4
6.  ~Cx                               Simp 4
7.  (∃x)Ax                           EG 5
8.  (∃x)Bx ∨ (x)Cx                   MP 1, 7
9.  ~(x)Cx                           DN 6
10. (∃x)~Cx                          QN 9
11. (x)Fx ⊃ (x)~Bx                   MP 3, 9
12. ~(x)~Bx ⊃ ~(x)Fx                  Contra 11
13. (∃x)Bx ∨ (∃x)~Bx                 Tautology
14. (x)Cx ∨ ~(x)Cx                  Tautology
15. (∃x)Bx ∨ ~(x)Cx                 Add 8
16. (∃x)Bx ∨ (∃x)~Cx                 Replace 10, 15
17. (∃x)~Bx ∨ (∃x)Bx                 Comm 16
18. (∃x)~Bx                          DS 10, 16
19. ~(x)Fx                           MP 12, 18
20. (∃x)~Fx                          QN 19
```