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Mirrors > Home > MPE Home > Th. List > nannot | Structured version Visualization version GIF version |
Description: Negation in terms of alternative denial. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Revised by Wolf Lammen, 26-Jun-2020.) |
Ref | Expression |
---|---|
nannot | ⊢ (¬ 𝜑 ↔ (𝜑 ⊼ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nanimn 1483 | . 2 ⊢ ((𝜑 ⊼ 𝜑) ↔ (𝜑 → ¬ 𝜑)) | |
2 | pm4.8 395 | . 2 ⊢ ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑) | |
3 | 1, 2 | bitr2i 278 | 1 ⊢ (¬ 𝜑 ↔ (𝜑 ⊼ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 208 ⊼ wnan 1480 |
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 209 df-an 399 df-nan 1481 |
This theorem is referenced by: nanbi 1489 trunantru 1574 falnanfal 1577 nic-dfneg 1667 andnand1 33744 imnand2 33745 |
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