In general, the conclusion will depend on all assumptions not discharged by the end. In particular, your conclusion still depends on the assumptions A -> B (your line 4 is not an actual application of (- I), so that assumption is not discharged), B -> A and -(A -> B).
Assumptions may be discharged exactly in the cases the rules tell you: The antecedent in a (-> I), the unnegated assumption in a (- I), the negated assumption in a (RAA), the disjuncts in a (v E).
Try to approach your proof more systematically. For example, on lines 3 to 5 you are deriving A -> B... from the assumption A -> B, which you already have on line 2. You can spare yourself this kind of detour and just work with the assumption straightaway. Always keep in mind what you're currently trying to prove.
Your current approach won't lead to success, because you never actually derive a contradiction that would make it possible to introduce a negation which allows you to discharge an assumption.
It is a useful technique to work by the hourglass strategy: Start your proof backwards, disassembling the conclusion by reverse applications of introduction rules on the main operator until you can get no further, then switch to the top and work your way down from the premises by successive applications of elimination rules until you hopefully meet in the middle. Eventually, you will have a kind of hourglass shape on the complexity of formulas, with long-ish formulas (the premises) on the top, successively dissected by elimination rules to smaller pieces in the middle, followed by introduction rules reassembling the information back to a new complex formula (the conclusion) at the bottom. First half (E) rules, second half (I) rules. This is what most non-detoured natural deduction proofs will look like, and it helps in finding your proof to try and achieve that shape.
You want to prove a conditional
-(A -> B) -> -(A <-> B), so the last step to have happend is likely an application of
(-> I) means you assume the antecedent (
-(A -> B)) and from that derive the succedent (
-(A <-> B)), after which you can discharge the assumption
-(A -> B).
Next on how to derive
-(A <-> B). The main operator is a negation, so the second-to-last step is likely a
(- I). That means you assume the unnegated formula
A <-> B, derive a contradiction from it, and hence conclude the negation
-(A <-> B), thereby discharging the assumption
A <-> B.
Informally, the proof proceeds as follows:
-(A -> B).
A <-> B.
- Then in particular,
A -> B.
- But by assumption
-(A -> B); contradiction.
- So the assumption
A <-> B must have been wrong, and it holds that
-(A <-> B).
- Since if
-(A -> B) then
-(A <-> B), we have
-(A -> B) -> -(A <-> B).
Can you translate this into a formal proof?
Also, you should probably explicitly mark your subproofs as such by adding indentation and vertical lines every time you open a new assumption level and visually exit it once the assumption is discharged (but this depends on how your teacher introduced the notation).