\begin{definition}[Definition:Proof System]
Let $\LL$ be a formal language.
A '''proof system''' $\mathscr P$ for $\LL$ comprises:
* '''Axioms''' and/or '''axiom schemata''';
* '''Rules of inference''' for deriving theorems.
It is usual that a '''proof system''' does this by declaring certain arguments concerning $\LL$ to be valid.
Informally, a '''proof system''' amounts to a precise account of what constitutes a '''(formal) proof'''.
\end{definition}