Using existential instantiation (logic) Am I using EI right on line 6? (Actually, I'm pretty sure the answer is 'no', and there's a few sketchy lines after that, too. So maybe you could also give a hint about how to do this). Prove: 1. (∃x)(∀y)(Gxy → Hxy) (Premise) 2. (∀x)(∃y)Hxy (Premise) ∴ (∀x)(∀y)Gxy 3. (∀y)(Gay → Hay) (1, Existential Instantiation) 4. Gab → Hab (3, Universal Instantiation) 5. (∃y)Hay (2, Universal Instantiation) 6. Hab (5, Existential Instantiation) 7. Gab (4, 6, Modus Tolens) 8. (∃y)Gay (7, Existential Generalization) 9. (∀y)Gay (8, Quantifier Negation) 10. (∃x)(∀y)Gxy (9, Existential Generalization) 11. (∀x)(∀y)Gxy (10, Quantifier Negation)

_The below is verbatim from a comment by Zhen Lin, which was requested by the OP to be posted as an answer, but that wasn't done._

_The primary intent of this answer is to remove this question from the Unanswered queue._

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Zhen Lin wrote:

> (6) is no good, because you introduced b in (4). But you have essentially the right idea: just put (4) after (6)!