ThmDex – An index of mathematical definitions, results, and conjectures.
De Morgan's laws are propositional tautologies
Formulation 0
Let $\phi, \psi \in \text{Proposition}$ each be a D2966: Propositional expression.
Then
(1) \begin{equation} \models \neg (\phi \lor \psi) \leftrightarrow \neg \phi \land \neg \psi \end{equation}
(2) \begin{equation} \models \neg (\phi \land \psi) \leftrightarrow \neg \phi \lor \neg \psi \end{equation}