SOLUTION: ((A & B) & C) & D, (D & C) → F, (B & C) → G, (A & D) → H ├ H & (G & F)

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Question 1209588: ((A & B) & C) & D, (D & C) → F, (B & C) → G, (A & D) → H ├ H & (G & F)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 1. ((A & B) & C) & D, 
 2. (D & C) → F, 
 3. (B & C) → G,
 4. (A & D) → H        ├ H & (G & F)

 5. (A & B) & C            1, Simplification
 6. A & B                  5, Simplification
 7. A                      6, Simplification  
 8. B & A                  6, Commutation
 9. B                      8, Simplification  
10. C & (A & B)            5, Commutation
11. C                     10, Simplification
12. D & ((A & B) & C)      1, Commutation
13. D                     12, Simplification
14. A & D               7,13, Conjunction
15. H                      4, Modus Ponens
16. B & C               9,11, Conjunction
17. G                   3,16, Modus ponens
18. D & C              13,11, Conjunction
19. F                   2,15, Modus Ponens
20. G & F              17,19, Conjunction
21. H & (G & F)        15,20, Conjunction

        
Edwin