1. (G -> H) -> J :. H -> J
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2. (~G v H) -> J 1 Material Implication
3. ~(~G v H) v J 2 Material Implication
4. (~~G * ~H) v J 3 De Morgan's Law
5. (G * ~H) v J 4 Double Negation
6. J v (G * ~H) 5 Commutation
7. (J v G) * (J v ~H) 6 Distribution
8. (J v ~H) * (J v G) 7 Commutation
9. J v ~H 8 Simplification
10. ~H v J 9 Commutation
11. H -> J 10 Material Implication
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