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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcin | Unicode version |
Description: The intersection of two bounded classes is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcdif.1 | BOUNDED |
bdcdif.2 | BOUNDED |
Ref | Expression |
---|---|
bdcin | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcdif.1 | . . . . 5 BOUNDED | |
2 | 1 | bdeli 13408 | . . . 4 BOUNDED |
3 | bdcdif.2 | . . . . 5 BOUNDED | |
4 | 3 | bdeli 13408 | . . . 4 BOUNDED |
5 | 2, 4 | ax-bdan 13377 | . . 3 BOUNDED |
6 | 5 | bdcab 13411 | . 2 BOUNDED |
7 | df-in 3108 | . 2 | |
8 | 6, 7 | bdceqir 13406 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wa 103 wcel 2128 cab 2143 cin 3101 BOUNDED wbdc 13402 |
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 13375 ax-bdan 13377 ax-bdsb 13384 |
This theorem depends on definitions: df-bi 116 df-clab 2144 df-cleq 2150 df-clel 2153 df-in 3108 df-bdc 13403 |
This theorem is referenced by: (None) |
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