Completeness of The Implicational Propositional Calculus
One reason that Peirce's law is important is that it can substitute for the law of excluded middle in the logic which only uses implication. The sentences which can be deduced from the axiom schemas:
- P→(Q→P)
- (P→(Q→R))→((P→Q)→(P→R))
- ((P→Q)→P)→P
- from P and P→Q infer Q
(where P,Q,R contain only "→" as a connective) are all the tautologies which use only "→" as a connective.
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