Fitch style proof of $(\neg B \to \neg A) \leftrightarrow (A \to B)$

Question

I have been stuck on this proof for a while. Here's where I'm at:

Goal $(\neg B \to \neg A) \leftrightarrow (A \to B)$

l 1. $A \to B$

ll 2. $\neg B$

lll 3. $A$

lll 4. $B$ Elim 1,3

lll 5. $\neg B$ Reit

ll 6. $A \to \neg B$ Into 3-5

ll 7. $\neg A$ ????

l $\neg B \to \neg A$ Into 2-7

If someone can help it will be great. Thank you

Answer 1

I don't get where you're going from step 6, but note the following.

In 4. you got $B$ and in the same subproof you got $\neg B$. You can infer a contradiction and proceed with $\neg$-$\text{Intro}$.

The other subproof should be similar.

Edit: See what I mean below.

Answer 2

Premises:

1. A ∨ B
2. C → ¬B
3. ¬C → ¬A
4. ¬B

Logical consequence: (A ↔ C)??