Reductio ad Absurdum

Proof Rule
The reductio ad absurdum is a valid deduction sequent in propositional logic:

Variants
The following forms can be used as variants of this theorem:

Also see

 * Clavius's Law


 * Proof by Contradiction, often treated as another aspect of the same thing.

From the point of view of purely classical logic, this is acceptable. However, in the context of intuitionistic logic, it is essential to bear in mind that only the Proof by Contradiction is valid.

This is because Proof by Contradiction starts with a positive assumption $\phi$.

As a result, it does not depend on the Law of Excluded Middle.