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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsbc | Unicode version |
Description: A formula resulting from proper substitution of a setvar for a setvar in a bounded formula is bounded. See also bdsbcALT 10650. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdcsbc.1 | BOUNDED |
Ref | Expression |
---|---|
bdsbc | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcsbc.1 | . . 3 BOUNDED | |
2 | 1 | ax-bdsb 10613 | . 2 BOUNDED |
3 | sbsbc 2819 | . 2 | |
4 | 2, 3 | bd0 10615 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wsb 1685 wsbc 2815 BOUNDED wbd 10603 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 ax-bd0 10604 ax-bdsb 10613 |
This theorem depends on definitions: df-bi 115 df-clab 2068 df-cleq 2074 df-clel 2077 df-sbc 2816 |
This theorem is referenced by: bdccsb 10651 |
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