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

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 $$\mathcal{F}$$.