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| Mirrors > Home > MPE Home > Th. List > nbfal | Structured version Visualization version GIF version | ||
| Description: The negation of a proposition is equivalent to itself being equivalent to ⊥. (Contributed by Anthony Hart, 14-Aug-2011.) |
| Ref | Expression |
|---|---|
| nbfal | ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fal 1554 | . 2 ⊢ ¬ ⊥ | |
| 2 | 1 | nbn 372 | 1 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥)) |
| Colors of variables: wff setvar class |
| Syntax hints: ¬ wn 3 ↔ wb 206 ⊥wfal 1552 |
| 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 207 df-tru 1543 df-fal 1553 |
| This theorem is referenced by: nulmo 2713 eq0 4350 ab0 4380 eq0rdv 4407 rzal 4509 bisym1 36420 wl-1xor 37483 wl-1mintru1 37489 aisfina 46910 aifftbifffaibifff 46934 lindslinindsimp2 48380 |
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