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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdunexb | Unicode version |
Description: Bounded version of unexb 4439. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bdunex.bd1 |
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bdunex.bd2 |
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Ref | Expression |
---|---|
bdunexb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1 3282 |
. . . 4
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2 | 1 | eleq1d 2246 |
. . 3
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3 | uneq2 3283 |
. . . 4
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4 | 3 | eleq1d 2246 |
. . 3
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5 | vex 2740 |
. . . 4
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6 | vex 2740 |
. . . 4
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7 | 5, 6 | bj-unex 14320 |
. . 3
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8 | 2, 4, 7 | vtocl2g 2801 |
. 2
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9 | ssun1 3298 |
. . . 4
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10 | bdunex.bd1 |
. . . . 5
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11 | 10 | bdssexg 14305 |
. . . 4
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12 | 9, 11 | mpan 424 |
. . 3
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13 | ssun2 3299 |
. . . 4
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14 | bdunex.bd2 |
. . . . 5
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15 | 14 | bdssexg 14305 |
. . . 4
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16 | 13, 15 | mpan 424 |
. . 3
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17 | 12, 16 | jca 306 |
. 2
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18 | 8, 17 | impbii 126 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-pr 4206 ax-un 4430 ax-bd0 14214 ax-bdor 14217 ax-bdex 14220 ax-bdeq 14221 ax-bdel 14222 ax-bdsb 14223 ax-bdsep 14285 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3597 df-pr 3598 df-uni 3808 df-bdc 14242 |
This theorem is referenced by: (None) |
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