How to convert a Gentzen Calculus Formula to a Natural Deduction One

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I have a proof on my textbook, which prooves denials of quantified propositions ∀xφ ⊨ ¬∃x¬φ... However it is written in Gentzen calculus style, while what I need it a Natural Deduction style one.

Click here to see the proof

Can you guys tell me what you think about the correction of the proofs in natural deduction?

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