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Inversion of Negation

Proposition: For every formula A, we have

~~A iff A.

Proof: Let A be an arbitrary formula. We have to show that the meaning of ~~A is the same as the meaning of A, i.e., that they have the same truth values.

A ~A ~~A
false true false
true false true

Since the last column coincides with the first column, we are done.

Author: Wolfgang Schreiner
Last Modification: October 6, 1999

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