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Theorem notnot 282
Description: Double negation. Theorem *4.13 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
notnot (φ ↔ ¬ ¬ φ)

Proof of Theorem notnot
StepHypRef Expression
1 notnot1 114 . 2 (φ → ¬ ¬ φ)
2 notnot2 104 . 2 (¬ ¬ φφ)
31, 2impbii 180 1 (φ ↔ ¬ ¬ φ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  notbid  285  con2bi  318  con1bii  321  imor  401  iman  413  dfbi3  863  alex  1572  19.8wOLD  1693  sbn  2062  difsnpss  3851  dfimak2  4298
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