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 $\textrm{TP}$.

It is also known as the Rule of Contraposition.

This can of course 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 the Law of the Excluded Middle. This axiom is not accepted by the intuitionist school.