\begin{definition}[Definition:Proof System/Rule of Inference]
Let $\LL$ be a formal language.
Part of defining a proof system $\mathscr P$ for $\LL$ is to specify its '''rules of inference'''.
A '''rule of inference''' is a specification of a valid means to conclude new theorems in $\mathscr P$ from given theorems and axioms of $\mathscr P$.
Often, the formulation of '''rules of inference''' also appeals to the notion of provable consequence.
\end{definition}