User:Lord Farin/Backup/Definition:Proof System/Rule of Inference

Definition
Let $\mathcal F$ be a formal system consisting of a formal language with deductive apparatus $\mathcal D$.

A rule of inference is a specification of a valid means to conclude new theorems in $\mathcal F$ from given theorems and axioms of $\mathcal F$.

Example
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.