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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdfal | GIF version |
Description: The truth value ⊥ is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdfal | ⊢ BOUNDED ⊥ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdtru 15329 | . . 3 ⊢ BOUNDED ⊤ | |
2 | 1 | ax-bdn 15314 | . 2 ⊢ BOUNDED ¬ ⊤ |
3 | df-fal 1370 | . 2 ⊢ (⊥ ↔ ¬ ⊤) | |
4 | 2, 3 | bd0r 15322 | 1 ⊢ BOUNDED ⊥ |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ⊤wtru 1365 ⊥wfal 1369 BOUNDED wbd 15309 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-bd0 15310 ax-bdim 15311 ax-bdn 15314 ax-bdeq 15317 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 |
This theorem is referenced by: bdnth 15331 bj-axemptylem 15389 |
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