Double Negation/Double Negation Elimination/Proof Rule

Theorem
The rule of double negation elimination is a valid argument in certain types of logic dealing with negation $\neg$.

This includes classical propositional logic and predicate logic, and in particular natural deduction, but for example not intuitionistic propositional logic.

As a proof rule it is expressed in the form:
 * If we can conclude $\neg \neg \phi$, then we may infer $\phi$.

It can be written:
 * $\ds {\neg \neg \phi \over \phi} \neg \neg_e$

Also see

 * This is a rule of inference of the following proof systems:
 * Definition:Natural Deduction