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Mirrors > Home > MPE Home > Th. List > notfal | Structured version Visualization version GIF version |
Description: A ¬ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) |
Ref | Expression |
---|---|
notfal | ⊢ (¬ ⊥ ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fal 1482 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | bitru 1487 | 1 ⊢ (¬ ⊥ ↔ ⊤) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 195 ⊤wtru 1476 ⊥wfal 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 196 df-tru 1478 df-fal 1481 |
This theorem is referenced by: trunanfal 1516 falnanfal 1518 truxorfal 1520 ifpdfnan 36850 |
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