Sorry for maybe a silly question but i need to understand how ¬(¬∀x ¬A(x)) equals ∀x ¬A(x)
In my mind, the negation before the parenthesis will be applied to both ¬∀x and ¬A(x). So it would look like this:
¬(¬∀x ¬A(x)) = ¬¬∀x ¬¬A(x)
A double negation would become positive and would then let ¬(¬∀x ¬A(x)) equal to ∀x A(x).
So, why would ¬(¬∀x ¬A(x)) equal ∀x ¬A(x)? Why wouldnt ¬(¬∀x ¬A(x)) equal ∀x A(x)?