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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 14964. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdcsbc.1 |
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Ref | Expression |
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bdsbc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcsbc.1 |
. . 3
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2 | 1 | ax-bdsb 14927 |
. 2
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3 | sbsbc 2978 |
. 2
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4 | 2, 3 | bd0 14929 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-4 1520 ax-17 1536 ax-ial 1544 ax-ext 2169 ax-bd0 14918 ax-bdsb 14927 |
This theorem depends on definitions: df-bi 117 df-clab 2174 df-cleq 2180 df-clel 2183 df-sbc 2975 |
This theorem is referenced by: bdccsb 14965 |
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