# Proof by Contradiction/Also known as

## Proof Rule

**Proof by Contradiction** is also known as **not-introduction**, and can be seen abbreviated as $\neg \mathcal I$ or $\neg_i$.

However, there are technical reasons why this form of abbreviation are suboptimal on this website, and **PBC** (if abbreviation is needed at all) is to be preferred.

It is also known as **proof of negation**, i.e., proof that some (positive!) assumption is not true.

Some sources do not explicitly distinguish between **Proof by Contradiction** and **Reductio ad Absurdum**, which starts with a negative assumption ($\neg \phi$).

Both can be referred to as **indirect proof**, but Reductio ad Absurdum is rejected by the intuitionistic school.