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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 2237 | . . . 4 |
3 | 2 | bdeq 13858 | . . 3 BOUNDED BOUNDED |
4 | 3 | albii 1463 | . 2 BOUNDED BOUNDED |
5 | df-bdc 13876 | . 2 BOUNDED BOUNDED | |
6 | df-bdc 13876 | . 2 BOUNDED BOUNDED | |
7 | 4, 5, 6 | 3bitr4i 211 | 1 BOUNDED BOUNDED |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1346 wceq 1348 wcel 2141 BOUNDED wbd 13847 BOUNDED wbdc 13875 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-ext 2152 ax-bd0 13848 |
This theorem depends on definitions: df-bi 116 df-cleq 2163 df-clel 2166 df-bdc 13876 |
This theorem is referenced by: bdceqi 13878 |
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