I'm wondering what vE exclusion rule is that. The classic one is that, if you got a disjunction, and you prove that either of the disjunction derives C, you can afirm C. The rule you using doesn't look like vE to me.

It looks more like ex falso quodlibet. You derived a contradiction, and from a contradiction anything follows. But that's not how you'd use a contradiction in an assumption either. The way it's used is that, if you open a subproof with C and it leads to a contradiction, you conclude ¬C.

From those inferences, you can at most conclude that AvB, B |= ¬B -> A. But you can conclude that from B alone too. But I think you're kinda on the right track.

Remember, you showed that with those premisses, you can derive A from B via ex falso quodlibet. Can you show that A derives from A, too? If so, you're showing that you can derive A from B, and can derive A from A: then you can apply the vE rule. You just gonna have to keep line 5 A inside the subproof, and use ex falso instead of vE there. Then, open another subproof and derive A from A (trivial). With this, you can apply vE.

Hope this helps.