Proofs Using Rules of Inferences (Natural Deduction Proofs)

Rules of Inferences

Argument Form

premise 1 premise 2 $⋮$ premise $n$

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$\therefore$ conclusion

Example

$\neg p\vee r$ $r\to s$ $\neg s$

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$\therefore \neg p$

How to prove that $\neg p$ is true?

Disjunctive Syllogism tells us $p\vee q$ $\neg p$

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$\therefore q$