Does $r \implies \neg q$, $q$ give $\neg r$?

Question

In resolution, if we have a premise such as $r \implies \neg q$ and we know that $q$ is true, can we infer $\neg r$? If yes what is the rule called

Answer 1

$r \to \neg q$ is equivalent to $\neg r \lor \neg q$, so given $q$, resolution gives us $\neg r$.

Answer 2

If your perspective is one of resolution, then it's just an instance of the resolution rule itself. Then $r\implies \neg q$ is an abbreviation for $\neg r\lor \neg q$, and resolution applied to $\neg r\lor\neg q$ and $q$ gives $\neg r$.