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Mirrors > Home > ILE Home > Th. List > Mathboxes > bds | Unicode version |
Description: Boundedness of a formula resulting from implicit substitution in a bounded formula. Note that the proof does not use ax-bdsb 11070; therefore, using implicit instead of explicit substitution when boundedness is important, one might avoid using ax-bdsb 11070. (Contributed by BJ, 19-Nov-2019.) |
Ref | Expression |
---|---|
bds.bd |
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bds.1 |
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Ref | Expression |
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bds |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bds.bd |
. . . 4
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2 | 1 | bdcab 11097 |
. . 3
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3 | bds.1 |
. . . 4
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4 | 3 | cbvabv 2208 |
. . 3
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5 | 2, 4 | bdceqi 11091 |
. 2
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6 | 5 | bdph 11098 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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-io 663 ax-5 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 ax-bd0 11061 ax-bdsb 11070 |
This theorem depends on definitions: df-bi 115 df-nf 1393 df-sb 1690 df-clab 2072 df-cleq 2078 df-clel 2081 df-bdc 11089 |
This theorem is referenced by: (None) |
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