A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, III, 6 p. 448

The dog that bit the letter carrier is a large terrier. Ajax is a small dog. Therefore, Ajax did not bite the letter carrier. (Dx: x is a dog; Bx: x bit the letter carrier; Lx: x is large; Tx: x is a terrier; a: Ajax)

 

1.     (∃x){Dx • Bx • (y)[(Dy • By) ⊃ y =x] • Lx • Tx} 2.     Da • ~ La ∴ ~ Ba 3.     Dr • Br • (y)[(Dy • By) ⊃ y =r] • Lr • Tr 4.     (y)[(Dy • By) ⊃ y =r] Dr • Br • Lr • Tr 5.     (y)[(Dy • By) ⊃ y =r] 6.     (Da • Ba) ⊃ a =r 7.     Ba 8.     Da 9.     Da • Ba 10.  a = r 11. Lr • (y)[(Dy • By) ⊃ y =r] • Dr • Br • Tr 12. Lr 13. La 14. ~ La • Da 15. ~ La 16. La • ~ La 17. ~ Ba

1 EI 3 Com 4 Simp 5 UI AIP 2 Simp 7,8 Conj 6,9 MP 3 Com 11 Simp 10,12 Id 2 Com 15 Simp 13,15 Conj 7-16 IP