Rule of Transposition/Formulation 1/Proof 1

Theorem

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

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 Aristotle, 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.