Symbolic Logic, Irving M. Copi, Prentice Hall, Fifth Edition, 1979, p. 150, problem 7

The argument is put as follows:

Adams and Brown were the only men at the banquet who drank. All the men at the banquet who brought liquor drank. Adams did not bring any liquor. If any man at the banquet drank, then some man at the banquet who drank must have brought liquor. All who drank became ill. Therefore, the man at the banquet who brought liquor became ill.

(a: Adams, b: Brown, Mx: was a man at the banquet, Dx: x drank, Lx: x brought liquor, Ix: x became ill). Symbolize and prove the validity.

1. (∃x){Mx • Dx • (y)[(My • Dy) ⊃ y = x] • (x = a ∨x = b)}
2. (x)[(Mx • Lx) ⊃Dx]
3. ¬ La
4. (∃x)(Mx • Dx) ⊃(∃x)(Mx • Dx • Lx)
5. (x)(Dx ⊃Ix)
6. ∴ (∃x){Mx • Lx • (y)[(My • Ly) ⊃y = x] • Ix}
7. Mm • Dm • (y)[(My • Dy) ⊃ y = m] • (m = a ∨m = b) / 1EI x/m
8. Mm • Dm / 7Simp.
9. (∃x)(Mx • Dx) / 8EG
10. (∃x)(Mx • Dx • Lx) / 9,4MP
11. Mr • Dr • Lr / 10EI x/r
12. * My • Ly / ACP
13. * (y)[(My • Dy) ⊃ y = m] / 7Simp.
14. * (My • Dy) ⊃ y = m / 13UI y/y
15. * (My • Ly) ⊃Dy / 2UI y/y
16. * Dy /12,15MP
17. * My /12Simp.
18. * My • Dy /16,17Conj.
19. * y = m /18,14MP
20. (My • Ly) ⊃y = m / 12-19CP
21. (y)[(My • Ly) ⊃y = m] / 20UG
22. Dm ⊃Im / 5UI x/m
23. Dm / 8Simp.
24. Im / 22,23MP
25. (y)[(My • Dy) ⊃ y = m] / 7Simp.
26. (Mr • Dr) ⊃ r = m / 25UI y/r
27. Mr • Dr / 11Simp.
28. r = m / 27,26MP
29. Lr / 11Simp.
30. Lm / 28,29Id
31. Mm / 8Simp.
32. Mm • Lm • (y)[(My • Ly) ⊃y = m] • Im / 31,30,25,24Conj.
33. (∃x){Mx • Lx • (y)[(My • Ly) ⊃y = x] • Ix} / 32EG