The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.6E, 3(a), p. 572

We have to show that: (x)[x = x ∨¬ (x = x)] is a theorem. There are a number of ways we could go. I choose this:

1. * ¬ (x = x) ......... ACP
2. * ¬ (x = x) ∨ x = x ......... Add.
3. * ¬ (x = x) ......... 1,2 DS
4. ¬ (x = x) ⊃¬ (x = x) ......... 1-3 CP
5. ¬ ¬ (x = x) ∨¬ (x = x) ......... 4 MI
6. x = x ∨¬ (x = x) ......... 5 DN
7. (x)[x = x ∨¬ (x = x)] ......... 6 UG