The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.6E, 4(b), p. 572

The argument:

"Hyde killed some innocent person. But Jekyll is Hyde. Jekyll is a doctor. Hence, some doctor killed some innocent person."

The proof, with the universe of discourse being 'persons':

1. (∃x)(Ix • Khx)
2. j = h
3. Dj
4. ∴(∃x)[Dx • (∃y)(Iy • Kxy)]
5. Im • Khm ......... 1 EI x/m
6. Khm ......... 5 Simp.
7. Kjm ......... 3,6 Id
8. Im ......... 5 Simp.
9. Im • Kjm ......... 7,8 Conj.
10. (∃y)(Iy • Kjy) ......... 9 EG
11. Dj • (∃y)(Iy • Kjy) ......... 3,10 Conj.
12. (∃x)[Dx • (∃y)(Iy • Kxy)] ......... 11 EG