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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdceq | Unicode version |
Description: Equality property for the predicate BOUNDED. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdceq.1 |
Ref | Expression |
---|---|
bdceq | BOUNDED BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdceq.1 | . . . . 5 | |
2 | 1 | eleq2i 2206 | . . . 4 |
3 | 2 | bdeq 13021 | . . 3 BOUNDED BOUNDED |
4 | 3 | albii 1446 | . 2 BOUNDED BOUNDED |
5 | df-bdc 13039 | . 2 BOUNDED BOUNDED | |
6 | df-bdc 13039 | . 2 BOUNDED BOUNDED | |
7 | 4, 5, 6 | 3bitr4i 211 | 1 BOUNDED BOUNDED |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1329 wceq 1331 wcel 1480 BOUNDED wbd 13010 BOUNDED wbdc 13038 |
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-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-ext 2121 ax-bd0 13011 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 df-clel 2135 df-bdc 13039 |
This theorem is referenced by: bdceqi 13041 |
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