ThmDex – An index of mathematical definitions, results, and conjectures.

Result R4079 on D3521: Propositional logic

Modus tollendo ponens in propositional logic

Formulation 0

Let $\phi$ and $\psi$ each be a D5382: Proposition.

Then \begin{equation} \frac{\phi \lor \psi, \neg \phi}{\psi} \end{equation}

Formulation 1

Let $\phi$ and $\psi$ each be a D5382: Proposition.

Then \begin{equation} (\phi \lor \psi) \land \neg \phi \quad \rightarrow \quad \psi \end{equation}