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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 9979. (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 9942 | . 2 BOUNDED |
3 | sbsbc 2768 | . 2 | |
4 | 2, 3 | bd0 9944 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wsb 1645 wsbc 2764 BOUNDED wbd 9932 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 ax-bd0 9933 ax-bdsb 9942 |
This theorem depends on definitions: df-bi 110 df-clab 2027 df-cleq 2033 df-clel 2036 df-sbc 2765 |
This theorem is referenced by: bdccsb 9980 |
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