Rule of inference

Propositional calculus

If ${\displaystyle P}$ implies ${\displaystyle Q}$ and ${\displaystyle R}$ implies ${\displaystyle S}$ and either ${\displaystyle Q}$ is false or ${\displaystyle S}$ is false, then either ${\displaystyle P}$ or ${\displaystyle R}$ must be false.

${\displaystyle {\frac {P\to Q,R\to S,\neg Q\lor \neg S}{\therefore \neg P\lor \neg R}}}$