(related to Lemma: The Proving Principle by Contradiction)

We want to prove that proving principle by contradiction is a valid logical argument. * The proving principle by contradiction is can be formulated as $(\neg p\Rightarrow 0)\Rightarrow p.$ * We can reformulate the implication as a disjunction on the left side and get the expression $(p\vee 0)\Rightarrow 0.$ * Because $0$ is smallest in the Boolean algebra of the Boolean algebra in propositional logic $(B,\wedge,\vee,1,0)$, we get the expression $p\Rightarrow p.$ * By definition of a valid logical argument, $p\Rightarrow p$ is valid.

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