In propositional logic, double negative elimination (also called double negation elimination, double negative introduction, double negation introduction, double negation, or negation elimination^{[1]}^{[2]}^{[3]}) are two validrules of replacement. They are the inferences that if Ais true, then not not-A is true and its converse, that, if not not-A is true, then A is true. The rule allows one to introduce or eliminate a negationfrom a logical proof. The rule is based on the equivalence of, for example, It is false that it is not raining. and It is raining.

The double negation introduction rule is:

P ¬¬P

and the double negation elimination rule is:

¬¬P P

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