# propositional logic – Proving the validity of a sequent using Modus Tollens

Problem: Prove $$p rightarrow (q vee r), neg q, neg r vdash neg p$$ using Modus Tollens.

I need to prove the validity of the above sequent by using natural deduction. Initially, I didn’t read the entire problem, and went the long way by doing an implication-elimination, two negation-eliminations, an or-elimination, and finally a negation-introduction. Then I read the problem and realized I had to use MT, and now I’m stuck. I don’t have the greatest grasp on propositional logic and natural deduction. Am I allowed to do the following?

Since I have $$neg q$$ and $$neg r$$ as my premises, can I use an and-introduction and do $$neg q wedge neg r$$, which would allow me to immediately use MT to deduce $$neg p$$? If not, could someone point me in the correct direction? Thanks.