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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcdif | Unicode version |
Description: The difference of two bounded classes is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcdif.1 | BOUNDED |
bdcdif.2 | BOUNDED |
Ref | Expression |
---|---|
bdcdif | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcdif.1 | . . . . 5 BOUNDED | |
2 | 1 | bdeli 13841 | . . . 4 BOUNDED |
3 | bdcdif.2 | . . . . . 6 BOUNDED | |
4 | 3 | bdeli 13841 | . . . . 5 BOUNDED |
5 | 4 | ax-bdn 13812 | . . . 4 BOUNDED |
6 | 2, 5 | ax-bdan 13810 | . . 3 BOUNDED |
7 | 6 | bdcab 13844 | . 2 BOUNDED |
8 | df-dif 3123 | . 2 | |
9 | 7, 8 | bdceqir 13839 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wcel 2141 cab 2156 cdif 3118 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-4 1503 ax-17 1519 ax-ial 1527 ax-ext 2152 ax-bd0 13808 ax-bdan 13810 ax-bdn 13812 ax-bdsb 13817 |
This theorem depends on definitions: df-bi 116 df-clab 2157 df-cleq 2163 df-clel 2166 df-dif 3123 df-bdc 13836 |
This theorem is referenced by: bdcnulALT 13861 |
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