The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 4th Edition, 2004, 10.5E, problem 2(d), p. 562

The task: to show that the argument is valid. It is, indeed. In 7 easy steps we deduce the conclusion.

1. (z)(Lz ≡ Hz)
2. (x)¬(Hx ∨¬ Bx)
3. ∴¬ Lb
4. (z)[(Lz ⊃Hz) • (Hz ⊃Lz)] ......... 1BE
5. ¬(Hb ∨¬ Bb) ......... 2UI x/b
6. ¬ Hb • Bb ......... 5DeM
7. ¬ Hb ......... 6Simp.
8. (Lb ⊃Hb) • (Hb ⊃Lb) ......... 4UI z/b
9. Lb ⊃Hb ......... 8Simp.
10. ¬ Lb ......... 7,9MT