I am trying to prove that $\neg A \to \bot \vdash A$, I can only use double negation elimination to get the conclusion, but I don't know how to prove double negation elimination.
Below is my proof for $\neg A \to \bot \vdash A$:
1 $\neg A\to\bot$
2 $\neg A$ (assumption)
3 $\bot$ ($\to$e 1, 2)
4 $\neg\neg A$ ($\neg$i 2-3)
5 $A$ (DNE 4)
The rules that can be used would be the basic rules of natural deduction: