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Double negation is a rule of inference and rule of replacement for classical propositional logic. It states that the negation of a negation of a proposition is logically equivalent to the affirmation of that proposition. [1][2] It is often expressed symbolically as so:

$\lnot \lnot P \Leftrightarrow P$

or even

$\lnot \lnot P = P$.

Where $\Leftrightarrow$ means "replaceable".

In standard rule form, this rule may be represented as two subrules:

$\frac {\lnot \lnot P} {P} , \frac{P}{\lnot \lnot P}$

Please note it is not universally accepted. Some formulations of propositional logic omit this rule of inference (such as intuitionistic propositional logic).

Natural Deduction Transformation Rules
Rules of Transformation

## ReferencesEdit

1. Double negation rule. Retrevied January 27, 2017 from http://www.philosophy-index.com/logic/forms/double-negation.php.
2. Double Negation. Retrieved January 27 2017 from http://lc.brooklyn.cuny.edu/smarttutor/logic/dubneg.html.