Understanding Symbolic Logic, Virginia Klenk, 5th ed., Pearson Prentice Hall, 2008, Unit 18, Ex. 2e, p. 354

Prove the logical truth.

1.     (∃y)[Fy • (x)(Gx ⊃ Hxy)] 2.     Gx 3.     Fm • (x)(Gx ⊃ Hxm)] 4.     (x)(Gx ⊃ Hxm)] • Fm 5.     (x)(Gx ⊃ Hxm) 6.     Gx ⊃ Hxm 7.     Hxm 8.     Fm 9.     Fm • Hxm 10.  (∃y)(Fy • Hxy)] 11.  Gx ⊃ (∃y)(Fy • Hxy)] 12.  (x)[Gx ⊃ (∃y)(Fy • Hxy)] 13.  (∃y)[Fy • (x)(Gx ⊃ Hxy)] ⊃ (x)[Gx ⊃ (∃y)(Fy • Hxy)]

(∃y)[Fy • (x)(Gx ⊃ Hxy)] ⊃ (x)[Gx ⊃ (∃y)(Fy • Hxy)] ACP ACP 1 EI 3 Com 4 Simp 5 UI 2,6 MP 3 Simp 7,8 Conj 9 EG 2-10 CP 11 UG 1-12 CP