In propositional logic, double negative elimination (also called double negation elimination, double negative introduction, double negation introduction, double negation, or negation elimination) 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:
and the double negation elimination rule is:
If I can say without immodesty, I am the talk of the town