Rule of Transposition/Formulation 1/Reverse Implication/Proof

Theorem

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

Proof
By the tableau method of natural deduction:

Law of Excluded Middle
Note that 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.