The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.6E, 1(c), p. 571

Show that [¬ (a = b) • b = c] ⊃ ¬ (a = c) is a theorem.

1. * ¬ (a = b) ......... ACP
2. * * b = c ......... ACP
3. * * ¬ (a = c)
4. * b = c ⊃ ¬ (a = c) ......... 2-3 CP
5. ¬ (a = b) ⊃ [b = c ⊃ ¬ (a = c)] ......... 1-4 CP
6. [¬ (a = b) • b = c] ⊃ ¬ (a = c) ......... 5 Exp.