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Mirrors > Home > NFE Home > Th. List > notnot1 | GIF version |
Description: Converse of double negation. Theorem *2.12 of [WhiteheadRussell] p. 101. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 2-Mar-2013.) |
Ref | Expression |
---|---|
notnot1 | ⊢ (φ → ¬ ¬ φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (¬ φ → ¬ φ) | |
2 | 1 | con2i 112 | 1 ⊢ (φ → ¬ ¬ φ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: notnoti 115 con1d 116 con4i 122 notnot 282 biortn 395 pm2.13 407 eueq2 3010 ifnot 3700 |
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