The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.6E, 2(c), p. 572

The task - to show that the argument is valid:

1. (z)[Gz ⊃(y)(Ky ⊃ Hzy)]
2. (Ki • Gj) • i = j
3. ∴ Hii
4. Gj ......... 2 Simp.
5. Gj ⊃(y)(Ky ⊃ Hjy) ......... 1 UI z/j
6. (y)(Ky ⊃ Hjy) ......... 4,5 MP
7. Ki ......... 2 Simp.
8. Ki ⊃Hji ......... 6 UI y/i
9. Hji ......... 7,8 MP
10. i = j ......... 2 Simp.
11. Hii ......... 9,10 Id