Double Negation rules of replacement

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How do I use double negation in rules of replacement?

Feb 23rd, 2015

In propositional logicdouble negative elimination (also called double negation eliminationdouble negative introductiondouble negation introductiondouble negation, or negation elimination[1][2][3]) are two valid rules 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:

\Leftrightarrow ¬¬P

and the double negation elimination rule is:

¬¬P \Leftrightarrow P
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Feb 23rd, 2015

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