Proof
(related to Lemma: The Proving Principle By Contraposition, Contrapositive)
- We have already shown, that every contraposition of an implication is equivalent that implication , formally $$(\neg p\Rightarrow \neg q)\Longrightarrow (p\Rightarrow q).$$
- In particular, the proving principle follows: $$(\neg p\Rightarrow \neg q)\Rightarrow(p\Rightarrow q).$$
- Since the right side is true if the left side is true, the proving principle $(\neg p\rightarrow \neg q)\Longrightarrow (p\Rightarrow q)$ is by definition a valid logical argument.
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