I have been working on this proof but I feel like I am stuck in a loop in the end and cannot get one step to be logically out of the sub proof. I have the premise $P \lor \lnot P$ and need to prove $(P \to Q) \to ((\lnot P \to Q) → Q)$.
This is what I have as a complete proof but as I mentioned, just the one line is causing me from having a non valid conclusion. I have left it as a REIT after trying many options. Can someone explain where I may be going wrong in my proof and how I can get that one line to work accordingly?
PS. I am doing my Bsc in Computer Science via correspondence and it has been very challenging teaching myself Formal Logic. Any comments and advice would be greatly appreciated!
HINT
The goal of the subproof is $(\neg P \rightarrow Q) \rightarrow Q$, which is a conditional, so try and set it up as another conditional proof, i.e.: