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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcun | Unicode version |
Description: The union of two bounded classes is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcdif.1 |
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bdcdif.2 |
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Ref | Expression |
---|---|
bdcun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcdif.1 |
. . . . 5
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2 | 1 | bdeli 14480 |
. . . 4
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3 | bdcdif.2 |
. . . . 5
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4 | 3 | bdeli 14480 |
. . . 4
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5 | 2, 4 | ax-bdor 14450 |
. . 3
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6 | 5 | bdcab 14483 |
. 2
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7 | df-un 3133 |
. 2
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8 | 6, 7 | bdceqir 14478 |
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 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-17 1526 ax-ial 1534 ax-ext 2159 ax-bd0 14447 ax-bdor 14450 ax-bdsb 14456 |
This theorem depends on definitions: df-bi 117 df-clab 2164 df-cleq 2170 df-clel 2173 df-un 3133 df-bdc 14475 |
This theorem is referenced by: bdcpr 14505 bdctp 14506 bdcsuc 14514 |
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