\begin{definition}[Definition:Independent Proof System]
Let $\LL$ be a logical language.
Let $\mathscr P$ be a proof system.
Then $\mathscr P$ is '''independent''' if it is not possible to derive one axiom or rule of inference of $\mathscr P$ from the others.
{{stub|Deliberately vague, as the context in which this definition was originally couched was equally vague. Needs to be made rigorous, or merged with pages building a more comprehensive treatment.}}
\end{definition}