Rule of Inference/Examples/Modus Ponendo Ponens

Example of Rule of Inference

In the context of propositional logic, an example of a rule of inference is:

If $p$ is a theorem, and $p \implies q$ is a theorem, then $q$ is a theorem.

which expresses Modus Ponendo Ponens.

Sources

• 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{I}$: 'NOT' and 'IF': $\S 3$
• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\text{II}.10$ Formal Proofs