Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(2)

Prove valid:

1. (x)(Px ⊃ Qx)
2. (x)(Qx ⊃ Rx)
3. Pa • ¬ Rb
4. ∴ a ≠ b
5. Pa ⊃ Qa ......... 1 UI x/a
6. Pa ......... 3 Simp.
7. Qa ......... 5,6 MP
8. Qa ⊃ Ra ......... 2 UI x/a
9. Ra ......... 7,8 MP
10. ¬ Rb ......... 3 Simp.
11. a ≠ b ......... 9,10 Id