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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdciin | Unicode version |
Description: The indexed intersection of a bounded class with a setvar indexing set is a bounded class. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdciun.1 | BOUNDED |
Ref | Expression |
---|---|
bdciin | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdciun.1 | . . . . 5 BOUNDED | |
2 | 1 | bdeli 13033 | . . . 4 BOUNDED |
3 | 2 | ax-bdal 13005 | . . 3 BOUNDED |
4 | 3 | bdcab 13036 | . 2 BOUNDED |
5 | df-iin 3811 | . 2 | |
6 | 4, 5 | bdceqir 13031 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cab 2123 wral 2414 ciin 3809 BOUNDED wbdc 13027 |
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 2119 ax-bd0 13000 ax-bdal 13005 ax-bdsb 13009 |
This theorem depends on definitions: df-bi 116 df-clab 2124 df-cleq 2130 df-clel 2133 df-iin 3811 df-bdc 13028 |
This theorem is referenced by: (None) |
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