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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 2224 | . . . 4 |
3 | 2 | bdeq 13398 | . . 3 BOUNDED BOUNDED |
4 | 3 | albii 1450 | . 2 BOUNDED BOUNDED |
5 | df-bdc 13416 | . 2 BOUNDED BOUNDED | |
6 | df-bdc 13416 | . 2 BOUNDED BOUNDED | |
7 | 4, 5, 6 | 3bitr4i 211 | 1 BOUNDED BOUNDED |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1333 wceq 1335 wcel 2128 BOUNDED wbd 13387 BOUNDED wbdc 13415 |
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 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-4 1490 ax-17 1506 ax-ial 1514 ax-ext 2139 ax-bd0 13388 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 df-clel 2153 df-bdc 13416 |
This theorem is referenced by: bdceqi 13418 |
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