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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdccsb | Unicode version |
Description: A class resulting from proper substitution of a setvar for a setvar in a bounded class is bounded. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdccsb.1 | BOUNDED |
Ref | Expression |
---|---|
bdccsb | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdccsb.1 | . . . . 5 BOUNDED | |
2 | 1 | bdeli 13563 | . . . 4 BOUNDED |
3 | 2 | bdsbc 13575 | . . 3 BOUNDED |
4 | 3 | bdcab 13566 | . 2 BOUNDED |
5 | df-csb 3041 | . 2 | |
6 | 4, 5 | bdceqir 13561 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wcel 2135 cab 2150 wsbc 2946 csb 3040 BOUNDED wbdc 13557 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 ax-ext 2146 ax-bd0 13530 ax-bdsb 13539 |
This theorem depends on definitions: df-bi 116 df-clab 2151 df-cleq 2157 df-clel 2160 df-sbc 2947 df-csb 3041 df-bdc 13558 |
This theorem is referenced by: (None) |
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