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

From ProofWiki
Jump to navigation Jump to search


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


By the tableau method of natural deduction:

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