Symbolic Logic, D. Jacquette, Wadsworth, 2001, Chpt. 8, IV(18), p. 436

The argument:

"All giraffes are long-necked mammals of the African plains. Therefore, the tonsils of a giraffe are the tonsils of a long-necked mammal of the African plains."

The proof:

1. (x)[Gx ⊃(Lx • Mx • Pxa)]
2. ∴(x)(y)[(Gy • Txy) ⊃ (∃z)(Lz • Mz • Pza • Txz)]
3. * Gy • Txy ......... ACP
4. * Gy ......... 3 Simp.
5. * Gy ⊃(Ly • My • Pya) ......... 1 UI x/y
6. * Ly • My • Pya ......... 4,5 MP
7. * Txy ......... 3 Simp.
8. * Ly • My • Pya • Txy ......... 6,7 Conj.
9. * (∃z)(Lz • Mz • Pza • Txz) ......... 8 EG
10. (Gy • Txy) ⊃ (∃z)(Lz • Mz • Pza • Txz) ......... 3-9 CP
11. (y)[(Gy • Txy) ⊃ (∃z)(Lz • Mz • Pza • Txz)] ......... 10 UG
12. (x)(y)[(Gy • Txy) ⊃ (∃z)(Lz • Mz • Pza • Txz)] ......... 11 UG