Rule of Transposition/Formulation 1

Theorem
A statement and its contrapositive have the same truth value:


 * $p \implies q \dashv \vdash \neg q \implies \neg p$

Its abbreviation in a tableau proof is $\textrm{TP}$.

This can be expressed as two separate theorems:

Law of the Excluded Middle
The proof of the reverse implication depends on the Law of the Excluded Middle, by way of Double Negation Elimination.

This is one of the axioms of logic that was determined by, and forms part of the backbone of classical (Aristotelian) logic.

However, the intuitionist school rejects the Law of the Excluded Middle as a valid logical axiom. This in turn invalidates the proof of the reverse implication from an intuitionistic perspective.

Also known as
The Rule of Transposition is also known as the Rule of Contraposition.

Also see

 * Definition:Contrapositive