Prove $$[(p→q) \wedge (qr→s)]\to [pr→s],$$ which is the same as $$[(\lnot p\lor q) \wedge (\lnot (qr) \lor s)]\to [\lnot (pr) \lor s]$$

I believe it can just be done with algebra rules, but I got stuck at the end.

And this is not a programming question.

Thanks.