The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.4E, 2(d), p. 556

Show that the following derivability claim holds:

1. (x)Mx
2. ∴ (x)(¬ Mx ⊃Mx)
3. Mx ......... 1 UI x/x
4. Mx ∨¬ ¬ Mx ......... 3 Add.
5. ¬ ¬ Mx ∨ Mx ......... 4 Comm.
6. ¬ Mx ⊃ Mx ......... 5 MI
7. (x)(¬ Mx ⊃ Mx) ......... 6 UG