Rule of Transposition

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


 * $$p \Longrightarrow q \vdash \lnot q \Longrightarrow \lnot p$$
 * $$\lnot q \Longrightarrow \lnot p \vdash p \Longrightarrow q$$

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

Proof
This follows directly from Modus Tollendo Tollens:

$$\lnot q \Longrightarrow \lnot p \vdash p \Longrightarrow q$$:

Comment
Note that the second part of this proof 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.