The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.4E, 1(k), p. 556

We have to derive the conclusion from the one premise given:

1. (x)[Fx ⊃(∃y)Gxy]
2. ∴(x)[Fx ⊃(∃y)(Gxy ∨ ¬ Hxy)]
3. * Fx ......... ACP
4. * Fx ⊃(∃y)Gxy ......... 1 UI x/x
5. * (∃y)Gxy ......... 3,4 MP
6. * (∃y)Gxy ∨ ¬ Hxy ......... 5 Add.
7. Fx ⊃(∃y)(Gxy ∨ ¬ Hxy) ......... 3-6 CP
8. (x)[Fx ⊃(∃y)(Gxy ∨ ¬ Hxy)] ......... 7 UG