De Morgan's Laws (Logic)/Conjunction of Negations/Formulation 2/Reverse Implication

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$\paren {\neg \paren {p \lor q} } \implies \paren {\neg p \land \neg q}$


By the tableau method of natural deduction:

$\vdash \paren {\neg \paren {p \lor q} } \implies \paren {\neg p \land \neg q} $
Line Pool Formula Rule Depends upon Notes
1 1 $\neg \paren {p \lor q}$ Assumption (None)
2 1 $\neg p \land \neg q$ Sequent Introduction 1 De Morgan's Laws (Logic): Conjunction of Negations: Formulation 1
3 $\paren {\neg \paren {p \lor q} } \implies \paren {\neg p \land \neg q}$ Rule of Implication: $\implies \II$ 1 – 2 Assumption 1 has been discharged