# 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.