Theorems in propositional logic | Rules of inference

Transposition (logic)

In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated. It is the inference from the truth of "A implies B" to the truth of "Not-B implies not-A", and conversely. It is very closely related to the rule of inference modus tollens. It is the rule that where "" is a metalogical symbol representing "can be replaced in a proof with". (Wikipedia).

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Related pages

Obversion | If and only if | Negation | Double negation | Theorem | Hypothetical syllogism | Tautology (logic) | Propositional calculus | Contraposition | Hilbert system | Logical consequence | Denying the antecedent | Metalogic | Modus tollens | Material conditional | Consequent | Antecedent (logic) | Sequent | Contraposition (traditional logic) | Symbol (formal) | Commutative property | Inference | Affirming the consequent | Formal proof | Term logic | Principia Mathematica | Rule of replacement | Rule of inference | Formal system | Bertrand Russell | Immediate inference | Material implication (rule of inference) | Alfred North Whitehead | Validity (logic)