Destructive Dilemma/Formulation 1

Context
Natural deduction.

Definition
$$p \Longrightarrow q, r \Longrightarrow s \vdash \lnot q \lor \lnot s \Longrightarrow \lnot p \lor \lnot r$$

Its abbreviation in a tableau proof is $$\textrm{DD}$$.

Proof
This is proved by the tableau method: