Is modus tollens applicable when a premise contains additional information

Question

I have something similar to the below:

\begin{align} &1. \ p \to q \\ &2. \ \lnot q \land \lnot s \\ &\text{c} \colon \, \lnot p \end{align}

Is this still equivalent to modus tollens since the 2nd premise can only be true if $\lnot q$ is true, and will be false if not? I am not really sure how to treat the $s$ variable seeing as it is not included in the conclusion.

Answer 1

The reasoning is valid, but it would be clearer to describe it as being two steps:

1. From $\neg q \land \neg s$ conclude $\neg q$.

2. From $\neg q$ and $p\to q$ conclude $\neg p$.