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Mirrors > Home > ILE Home > Th. List > notfal | 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 1342 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | bitru 1347 | 1 ⊢ (¬ ⊥ ↔ ⊤) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 104 ⊤wtru 1336 ⊥wfal 1340 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 |
This theorem is referenced by: truxorfal 1402 falxortru 1403 falxorfal 1404 |
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