Modus Ponendo Ponens/Proof Rule/Tableau Form
Jump to navigation
Jump to search
Proof Rule
Let $\phi \implies \psi$ be a well-formed formula in a tableau proof whose main connective is the implication operator.
The Modus Ponendo Ponens is invoked for $\phi \implies \psi$ and $\phi$ as follows:
| Pool: | The pooled assumptions of $\phi \implies \psi$ | ||||||||
| The pooled assumptions of $\phi$ | |||||||||
| Formula: | $\psi$ | ||||||||
| Description: | Modus Ponendo Ponens | ||||||||
| Depends on: | The line containing the instance of $\phi \implies \psi$ | ||||||||
| The line containing the instance of $\phi$ | |||||||||
| Abbreviation: | $\text{MPP}$ or $\implies \EE$ |
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $2$ Conditionals and Negation