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 Excluded Middle
Note that the proof of the reverse implication requires the use of double negation elimination, which depends on Law of Excluded Middle. This axiom is not accepted by the intuitionist school.

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

Also see

 * Definition:Contrapositive