Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > bdstab | GIF version |
Description: Stability of a bounded formula is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdstab.1 | ⊢ BOUNDED 𝜑 |
Ref | Expression |
---|---|
bdstab | ⊢ BOUNDED STAB 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdstab.1 | . . . . 5 ⊢ BOUNDED 𝜑 | |
2 | 1 | ax-bdn 9937 | . . . 4 ⊢ BOUNDED ¬ 𝜑 |
3 | 2 | ax-bdn 9937 | . . 3 ⊢ BOUNDED ¬ ¬ 𝜑 |
4 | 3, 1 | ax-bdim 9934 | . 2 ⊢ BOUNDED (¬ ¬ 𝜑 → 𝜑) |
5 | df-stab 740 | . 2 ⊢ (STAB 𝜑 ↔ (¬ ¬ 𝜑 → 𝜑)) | |
6 | 4, 5 | bd0r 9945 | 1 ⊢ BOUNDED STAB 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 STAB wstab 739 BOUNDED wbd 9932 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-bd0 9933 ax-bdim 9934 ax-bdn 9937 |
This theorem depends on definitions: df-bi 110 df-stab 740 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |