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 an element of that part of $\mathcal D$ which allows one to deduce whether or not a particular well-formed word of $\mathcal F$ is a theorem of $\mathcal F$.