Clavius's Law/Formulation 1/Proof 2

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From Peirce's Law:

$\left({p \implies q}\right) \implies p \vdash p$

follows Clavius's Law:

$\neg p \implies p \vdash p$


By the tableau method of natural deduction:

$\neg p \implies p \vdash p$
Line Pool Formula Rule Depends upon Notes
1 1 $\neg p \implies p$ Premise (None)
2 2 $p \implies \bot$ Assumption (None)
3 2 $\neg p$ Sequent Introduction 2 Negation as Implication of Bottom
4 1,2 $p$ Modus Ponendo Ponens: $\implies \mathcal E$ 1, 3
5 1 $(p \implies \bot) \implies p$ Rule of Implication: $\implies \II$ 2 – 4 Assumption 2 has been discharged
6 1 $p$ Sequent Introduction 5 Peirce's Law