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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcdif | Unicode version |
Description: The difference 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 |
---|---|
bdcdif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcdif.1 |
. . . . 5
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2 | 1 | bdeli 15084 |
. . . 4
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3 | bdcdif.2 |
. . . . . 6
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4 | 3 | bdeli 15084 |
. . . . 5
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5 | 4 | ax-bdn 15055 |
. . . 4
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6 | 2, 5 | ax-bdan 15053 |
. . 3
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7 | 6 | bdcab 15087 |
. 2
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8 | df-dif 3146 |
. 2
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9 | 7, 8 | bdceqir 15082 |
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 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 ax-ext 2171 ax-bd0 15051 ax-bdan 15053 ax-bdn 15055 ax-bdsb 15060 |
This theorem depends on definitions: df-bi 117 df-clab 2176 df-cleq 2182 df-clel 2185 df-dif 3146 df-bdc 15079 |
This theorem is referenced by: bdcnulALT 15104 |
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