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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 1306 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | bitru 1311 | 1 ⊢ (¬ ⊥ ↔ ⊤) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 104 ⊤wtru 1300 ⊥wfal 1304 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-fal 1305 |
This theorem is referenced by: truxorfal 1366 falxortru 1367 falxorfal 1368 |
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