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Natural deduction: negation of quantifiers

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Proof: $a = b \vdash f(a) = f(b)$

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Natural deduction predicate logic for equality

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natural deduction proof with De Morgan's laws

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Is this (tricky) natural deduction with De Morgan's laws correct?

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validity of conditional proof

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What's wrong with this natural deduction proof?

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Natural deduction : $\lnot \forall x.P(x) \to \exists x. \lnot P(x)$

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102
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Decision procedure for completeness for CPC with arbitrary natural deduction rules

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How can I prove $(P \to Q) \to (\lnot Q \to \lnot P)$?

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Natural deduction, Proof $\vdash$ $P\Rightarrow(Q\Rightarrow P)$

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prove that $\vdash (P \Rightarrow Q) \lor (Q \Rightarrow P)$

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Is negation introduction derivable in the natural deduction system of intuitionistic propositional logic?

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How to use natural deduction for introducing implication

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50
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natural deduction problem using the connective not

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