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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdph | Unicode version |
Description: A formula which defines (by class abstraction) a bounded class is bounded. (Contributed by BJ, 6-Oct-2019.) |
Ref | Expression |
---|---|
bdph.1 | BOUNDED |
Ref | Expression |
---|---|
bdph | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdph.1 | . . . . 5 BOUNDED | |
2 | 1 | bdeli 13841 | . . . 4 BOUNDED |
3 | df-clab 2157 | . . . 4 | |
4 | 2, 3 | bd0 13819 | . . 3 BOUNDED |
5 | 4 | ax-bdsb 13817 | . 2 BOUNDED |
6 | sbid2v 1989 | . 2 | |
7 | 5, 6 | bd0 13819 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wsb 1755 wcel 2141 cab 2156 BOUNDED wbd 13807 BOUNDED wbdc 13835 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-bd0 13808 ax-bdsb 13817 |
This theorem depends on definitions: df-bi 116 df-sb 1756 df-clab 2157 df-bdc 13836 |
This theorem is referenced by: bds 13846 |
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