Double negation law

Statement

In classical logic, for each proposition $p$, the proposition $\neg \neg p$ is logically equivalent to $p$. $$\neg \neg p \equiv p$$

Remarks

The implication $p \to \neg \neg p$ is also valid in intuitionistic logic. The other direction, $\neg \neg p \to p$, needs classical logic. This direction is the basis of proof by contradiction.

Explanations

L1 human

"It is not true that $5$ is not prime" says the same as "$5$ is prime". Two negations cancel each other.