\begin{definition}[Definition:Hilbert Proof System/Instance 1]
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This instance of a Hilbert proof system is used in:
* {{BookReference|Mathematical Logic for Computer Science|2012|M. Ben-Ari|ed=3rd|edpage=Third Edition}}
Let $\LL$ be the language of propositional logic.
$\mathscr H$ has the following axioms and rules of inference:
\end{definition}