In my course notes it is stated that we can infer $\exists x\neg F$ from $\neg\forall xF$ (where $F$ is a formula) in classical logic, but not in intuitionistic logic. However, I came up with this natural deduction $$ \cfrac{\cfrac{\cfrac{\quad}{F}\scriptstyle1}{\forall xF} \quad \begin{array}{c}\\\neg\forall xF\end{array}}{ \cfrac{\cfrac{\bot}{\neg F} \scriptstyle1}{\exists x \neg F} } $$ and it seems fine and intuitionistic to me... What am I missing?
2026-03-27 00:09:36.1774570176
Possible mistake in natural deduction
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