Axiom System
- Axiom schema 1 is P → (Q → P).
- Axiom schema 2 is (P → (Q → R)) → ((P → Q) → (P → R)).
- Axiom schema 3 (Peirce's law) is ((P → Q) → P) → P.
- The one non-nullary rule of inference (modus ponens) is: from P and P → Q infer Q.
Where in each case, P, Q, and R may be replaced by any formulas which contain only "→" as a connective. If Γ is a set of formulas and A a formula, then means that A is derivable using the axioms and rules above and formulas from Γ as additional hypotheses.
Read more about this topic: Implicational Propositional Calculus
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