Definition:Hilbert Proof System/Instance 1

Definition
 This instance of a Hilbert proof system is used in:



Let $\mathcal L$ be the language of propositional logic.

$\mathscr H$ has the following axioms and rules of inference:

Axioms
Let $\mathbf A, \mathbf B, \mathbf C$ be WFFs.

The following three WFFs are axioms of $\mathscr H$:

Rules of Inference
The sole rule of inference is Modus Ponendo Ponens:


 * From $\mathbf A$ and $\mathbf A \implies \mathbf B$, one may infer $\mathbf B$.