I\'ve been having trouble solving this proof, any help would be greatly apprecia

Question

I've been having trouble solving this proof, any help would be greatly appreciated!

a v b --> c, d --> (c' v b) ^ a, b' ^ d = ((a --> b v c) ^ d) --> (a ^ b ^ c ^ d)'

Explanation / Answer

I don't really know what you are trying to prove...and I'm assuming ' means not or ~. Again, correct me if I'm wrong. So assuming these two are premises. And you're trying to prove b' ^ d = ((a --> b v c) ^ d) --> (a ^ b ^ c ^ d)' 1. (a v b) --> c Given 2. d --> (c' v b) ^ a Given 3. ((a --> b v c) ^ d) --> (a ^ b ^ c ^ d)' Assume (You can start with either side) 4. Assume (a ^ b ^ c ^ d) For Contradiction 5. (a v b) 4. 6. c 1,5 7. (b v c) V introduction, 6 8. (a --> b v c) Conditional Introduction 9. ((a --> b v c) ^ d) Conjunction Intro. 10. (a ^ b ^ c ^ d)' 3,9 Elim. 11. (a ^ b ^ c ^ d) 4, Repitition 12. (a ^ b ^ c ^ d)' Contradiction (Get out of the assumption) 13. ((a --> b v c) ^ d) 12, 3 (There's a law/theorem for this) 14. d 13 15. (c' v b) ^ a 2, 14 16. a 15 17. (a v b) 16. 18. c 1,17 19. b 20. so we get b^d, but also (a ^ b ^ c ^ d) 21. So therefore, b^d cannot be true. --This is where I found issues. 22. so b' ^ d?

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