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Mirrors > Home > NFE Home > Th. List > notnot | GIF version |
Description: Double negation. Theorem *4.13 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
notnot | ⊢ (φ ↔ ¬ ¬ φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot1 114 | . 2 ⊢ (φ → ¬ ¬ φ) | |
2 | notnot2 104 | . 2 ⊢ (¬ ¬ φ → φ) | |
3 | 1, 2 | impbii 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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