# Definition:Theorem/Formal System

## Definition

Let $\LL$ be a formal language.

Let $\mathscr P$ be a proof system for $\LL$.

A theorem of $\mathscr P$ is a well-formed formula of $\LL$ which can be deduced from the axioms and axiom schemata of $\mathscr P$ by means of its rules of inference.

That a WFF $\phi$ is a theorem of $\mathscr P$ may be denoted as:

$\vdash_{\mathscr P} \phi$

## Also known as

A theorem $\phi$ of $\mathscr P$ is also called provable from $\mathscr P$.