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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 9966 | . . . 4 BOUNDED |
3 | 2 | ax-bdal 9938 | . . 3 BOUNDED |
4 | 3 | bdcab 9969 | . 2 BOUNDED |
5 | df-iin 3660 | . 2 | |
6 | 4, 5 | bdceqir 9964 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cab 2026 wral 2306 ciin 3658 BOUNDED wbdc 9960 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 ax-bd0 9933 ax-bdal 9938 ax-bdsb 9942 |
This theorem depends on definitions: df-bi 110 df-clab 2027 df-cleq 2033 df-clel 2036 df-iin 3660 df-bdc 9961 |
This theorem is referenced by: (None) |
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