Hilbert Proof System Definition The axioms of Hilbert system are all propositions of the following forms o(a→(→a) (a→(6→)→((a→B)→(a→7) (3→-a)→(6→a)→BHilbert Proof System . Definition . . The axioms of Hilbert system are all propositions of the following forms: 1. (α → (β → α)) 2. ((α → (β → γ)) → ((α → β) → (α → γ))) 3. (¬β → ¬α) → ((¬β → α) → β) Yi Li (Fudan University) Discrete Mathematics April 16, 2013 14 / 17