\begin{definition}[Definition:Axiom/Formal Systems]
Let $\LL$ be a formal language.
Part of defining a proof system $\mathscr P$ for $\LL$ is to specify its '''axioms'''.
An '''axiom of $\mathscr P$''' is a well-formed formula of $\LL$ that $\mathscr P$ approves of by definition.
\end{definition}