# Question about Fitch style natural deduction

So I have a proof in which i have derived both ~P and (P v Q). My current objective is to extract the Q as I need it for another part of the proof. It seems obvious to me that if I have ~P true and (P v Q) true, then Q is necessarily true. However, to get Q I would need to use the disjunction elimination rule, and I am unsure of how to insert that into my proof to get the desired result (Q). Any help would be appreciated

Indeed $$\neg P$$ and $$P\vee Q$$ do entail $$Q$$ by rule of Disjunctive Syllogism.
A contradiction may be derived when assuming $$P$$, since $$\neg P$$ is a premise, and $$Q$$ may be derived from that contradiction, since anything may.
Also $$Q$$ is trivially derived when assuming $$Q$$; it is what was assumed.
And from $$\neg P, P\vdash Q$$ and $$Q\vdash Q$$ we may infer $$\neg P,P\vee Q\vdash Q$$ ...
$$\def\fitch#1#2{\quad\begin{array}{|l}#1\\\hline#2\end{array}}\fitch{~~1.~\neg P\\~~2.~P\vee Q}{\fitch{~~3.~P}{~~4.~\bot\hspace{10ex}{\neg}\mathsf E~1,3\\~~5.~Q\hspace{10ex}\mathsf{X}~4}\\\fitch{~~6.~Q}{}\\~~7.~Q\hspace{14ex}{\vee}\mathsf E~2,3{-}5,6{-}6}$$