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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcun | Unicode version |
Description: The union of two bounded classes is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcdif.1 | BOUNDED |
bdcdif.2 | BOUNDED |
Ref | Expression |
---|---|
bdcun | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcdif.1 | . . . . 5 BOUNDED | |
2 | 1 | bdeli 13563 | . . . 4 BOUNDED |
3 | bdcdif.2 | . . . . 5 BOUNDED | |
4 | 3 | bdeli 13563 | . . . 4 BOUNDED |
5 | 2, 4 | ax-bdor 13533 | . . 3 BOUNDED |
6 | 5 | bdcab 13566 | . 2 BOUNDED |
7 | df-un 3115 | . 2 | |
8 | 6, 7 | bdceqir 13561 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wo 698 wcel 2135 cab 2150 cun 3109 BOUNDED wbdc 13557 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 ax-ext 2146 ax-bd0 13530 ax-bdor 13533 ax-bdsb 13539 |
This theorem depends on definitions: df-bi 116 df-clab 2151 df-cleq 2157 df-clel 2160 df-un 3115 df-bdc 13558 |
This theorem is referenced by: bdcpr 13588 bdctp 13589 bdcsuc 13597 |
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