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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdnth | GIF version |
Description: A falsity is a bounded formula. (Contributed by BJ, 6-Oct-2019.) |
Ref | Expression |
---|---|
bdnth.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
bdnth | ⊢ BOUNDED 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdfal 10624 | . 2 ⊢ BOUNDED ⊥ | |
2 | fal 1291 | . . 3 ⊢ ¬ ⊥ | |
3 | bdnth.1 | . . 3 ⊢ ¬ 𝜑 | |
4 | 2, 3 | 2false 649 | . 2 ⊢ (⊥ ↔ 𝜑) |
5 | 1, 4 | bd0 10615 | 1 ⊢ BOUNDED 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ⊥wfal 1289 BOUNDED wbd 10603 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-bd0 10604 ax-bdim 10605 ax-bdn 10608 ax-bdeq 10611 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 |
This theorem is referenced by: bdcnul 10656 |
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