Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
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 13202 | . 2 ⊢ BOUNDED ⊥ | |
2 | fal 1339 | . . 3 ⊢ ¬ ⊥ | |
3 | bdnth.1 | . . 3 ⊢ ¬ 𝜑 | |
4 | 2, 3 | 2false 691 | . 2 ⊢ (⊥ ↔ 𝜑) |
5 | 1, 4 | bd0 13193 | 1 ⊢ BOUNDED 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ⊥wfal 1337 BOUNDED wbd 13181 |
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 ax-bd0 13182 ax-bdim 13183 ax-bdn 13186 ax-bdeq 13189 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 |
This theorem is referenced by: bdcnul 13234 |
Copyright terms: Public domain | W3C validator |