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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 13191; therefore, using implicit instead of explicit substitution when boundedness is important, one might avoid using ax-bdsb 13191. (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 13218 |
. . 3
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3 | bds.1 |
. . . 4
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4 | 3 | cbvabv 2265 |
. . 3
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5 | 2, 4 | bdceqi 13212 |
. 2
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6 | 5 | bdph 13219 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-bd0 13182 ax-bdsb 13191 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-bdc 13210 |
This theorem is referenced by: (None) |
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