False Statement implies Every Statement/Formulation 2/Proof 2

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$\vdash \neg p \implies \paren {p \implies q}$


By the tableau method of natural deduction:

$\vdash \neg p \implies \left({p \implies q}\right)$
Line Pool Formula Rule Depends upon Notes
1 1 $\neg p$ Assumption (None)
2 1 $p \implies q$ Sequent Introduction 1 False Statement implies Every Statement: Formulation 1
3 $\neg p \implies \left({p \implies q}\right)$ Rule of Implication: $\implies \II$ 1 – 2 Assumption 1 has been discharged