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1. F -> G
2. F v G :. G
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3. G v F 2 Commutation
4. ~~G v F 3 Double Negation
5. ~G -> F 4 Material Implication
6. ~G -> G 5,1 Hypothetical Syllogism
7. ~~G v G 6 Material Implication
8. G v G 7 Double Negation
9. G 8 Tautology