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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcuni | Unicode version |
Description: The union of a setvar is a bounded class. (Contributed by BJ, 15-Oct-2019.) |
Ref | Expression |
---|---|
bdcuni | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bdel 13019 | . . . . 5 BOUNDED | |
2 | 1 | ax-bdex 13017 | . . . 4 BOUNDED |
3 | 2 | bdcab 13047 | . . 3 BOUNDED |
4 | df-rex 2422 | . . . . 5 | |
5 | exancom 1587 | . . . . 5 | |
6 | 4, 5 | bitri 183 | . . . 4 |
7 | 6 | abbii 2255 | . . 3 |
8 | 3, 7 | bdceqi 13041 | . 2 BOUNDED |
9 | df-uni 3737 | . 2 | |
10 | 8, 9 | bdceqir 13042 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wa 103 wex 1468 cab 2125 wrex 2417 cuni 3736 BOUNDED wbdc 13038 |
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-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-bd0 13011 ax-bdex 13017 ax-bdel 13019 ax-bdsb 13020 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-rex 2422 df-uni 3737 df-bdc 13039 |
This theorem is referenced by: bj-uniex2 13114 |
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