Got stuck while figuring out the formal proof for the following: $$\begin{array}{r} A\lor B\\ \neg B\lor C\\ \hline A\lor C \end{array}$$
The conclusion seems obvious. But finding a formal proof for it does not seem to be a trivial task for me.
I am trying to solve it via the backwards method. The conclusion is most likely to be derived via $\lor$Elim rule, but I cannot figure out how to derive it from the premises.
I will be grateful for any hints! Thank you!