$\forall x(Fx \lor \neg Fx) \rightarrow Ga \vdash \exists x Gx$
1) ∀x(Fx v ¬Fx) → Ga Premise
2)¬∃xGx Premise (Negation of conclusion)
3)∀x¬Gx Quantifier negation
4)¬Ga Universal installment
5)¬∀x(Fx v ¬Fx) Modus Tollens
6)...
I dont know how to do this derivation. My attempt might be ineffective. Some help/tips please? Thanks in advance :)
You're on the right track. I don't know if you have the inference rules to do this, But I would follow with:
$6. \exists x \neg (Fx \lor \neg Fx) \quad Quantifier \ Negation \ 5$
$7. \neg (Fb \lor \neg Fb) \quad Existential \ Installment \ 6$
$8. \neg Fb \land \neg \neg Fb \quad DeMorgan \ 7$
$9. \neg Fb \quad Simplification \ 8$
$10. \neg \neg Fb \quad Simplification \ 8$
$11. Fb \quad Double \ Negation \ 10$
$12. Contradiction \ 9,11$