Hey all,

I majored in Philosophy in college, and Logic was my concentration. Unfortunately, I have been out of practice for a long time. Recently, I've been trying to knock the rust off by working through Copi's Introduction to Logic 5ed. Could anyone help prove the following? I've been working on this one for way too long now.

1. ~F v ~[~(G•H) • (GvH)]
2. (G⊃H) ⊃ [(H⊃G) ⊃ I] //∴ F ⊃ (F•I)

Available Rules:
I. Rules of Inference (10)


1. Modus Ponens (M.P.):
P⊃Q
P
∴ Q

2. Modus Tollens (M.T.):
P⊃Q
∼Q
∴ ∼P

3. Disjunctive Syllogism (D.S.):
P˅Q
∼P
∴ Q

4. Constructive Dilemma (C.D.):
(P⊃Q) ˅ (R⊃S)
P˅R
∴ Q˅S

5. Destructive Dilemma (D.D.):
(P⊃Q) ˅ (R⊃S)
∼Q ˅ ∼S
∴ ∼P ˅ ∼R


6. Hypothetical Syllogism (H.S.):
P⊃Q
Q⊃R
∴ P⊃R

7. Simplification (simp.):
P•Q
∴ P


8. Conjunction (conj.):
P
Q
∴ P•Q


9. Addition (add.)
P
∴ P˅Q


10. Absorption (abs.):
P⊃Q
∴ P ⊃ (P•Q)

II. Rules of Replacement (11)


11. De Morgan’s Theorems (DeM.):
∼ (P˅Q) ≡ (∼P • ∼Q)
∼ (P•Q) ≡ (∼P ˅ ∼Q)

12. Commutation (comm.):
(P˅Q) ≡ (Q˅P)
(P•Q) ≡ (Q•P)

13. Association (assoc.):
[P ˅ (Q˅R)] ≡ [(P˅Q) ˅ R]
[P • (Q•R)] ≡ [(P•Q) • R]

14. Distribution (dist.):
[P • (Q˅R)] ≡ [(P•Q) ˅ (P•R)]
[P ˅ (Q•R)] ≡ [(PvQ) • (P˅R)]

15. Double Negation (D.N.): P ≡ ∼∼P

16. Transposition (trans.): (P⊃Q) ≡ (∼Q ⊃ ∼P)

17. Material Implication (imp.): (∼P ˅ Q) ≡ (P⊃Q)

18. Material Equivalence (equiv.):
(P≡Q) ≡ [(P⊃Q) • (Q⊃P)]
(P≡Q) ≡ [(P•Q) ˅ (∼P • ∼Q)]

19. Exportation (exp.): [(P•Q) ⊃ R] ≡ [P ⊃ (Q⊃R)]

20. Tautology (taut.):
P ≡ (P˅P)
P ≡ (P•P)

21. Negated Conditional (N.C.) ~(P⊃Q) ≡ P • ~Q