De Morgan's Laws (Logic)/Disjunction/Formulation 1/Forward Implication

Theorem

 * $p \lor q \vdash \neg \left({\neg p \land \neg q}\right)$

Proof

 * align="right" | 6 ||
 * align="right" | 2, 5
 * $\bot$
 * $\neg \mathcal E$
 * 5, 3
 * 5, 3


 * align="right" | 8 ||
 * align="right" | 2, 7
 * $\bot$
 * $\neg \mathcal E$
 * 7, 4
 * align="right" | 9 ||
 * align="right" | 1, 2
 * $\bot$
 * $\lor \mathcal E$
 * 1, 5-6, 7-8
 * align="right" | 10 ||
 * align="right" | 1
 * $\neg \left({\neg p \land \neg q}\right)$
 * Proof by Contradiction
 * 2, 9
 * align="right" | 10 ||
 * align="right" | 1
 * $\neg \left({\neg p \land \neg q}\right)$
 * Proof by Contradiction
 * 2, 9