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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdunexb | Unicode version |
Description: Bounded version of unexb 4195. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bdunex.bd1 | BOUNDED |
bdunex.bd2 | BOUNDED |
Ref | Expression |
---|---|
bdunexb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1 3119 | . . . 4 | |
2 | 1 | eleq1d 2147 | . . 3 |
3 | uneq2 3120 | . . . 4 | |
4 | 3 | eleq1d 2147 | . . 3 |
5 | vex 2604 | . . . 4 | |
6 | vex 2604 | . . . 4 | |
7 | 5, 6 | bj-unex 10710 | . . 3 |
8 | 2, 4, 7 | vtocl2g 2662 | . 2 |
9 | ssun1 3135 | . . . 4 | |
10 | bdunex.bd1 | . . . . 5 BOUNDED | |
11 | 10 | bdssexg 10695 | . . . 4 |
12 | 9, 11 | mpan 414 | . . 3 |
13 | ssun2 3136 | . . . 4 | |
14 | bdunex.bd2 | . . . . 5 BOUNDED | |
15 | 14 | bdssexg 10695 | . . . 4 |
16 | 13, 15 | mpan 414 | . . 3 |
17 | 12, 16 | jca 300 | . 2 |
18 | 8, 17 | impbii 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 wceq 1284 wcel 1433 cvv 2601 cun 2971 wss 2973 BOUNDED wbdc 10631 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-pr 3964 ax-un 4188 ax-bd0 10604 ax-bdor 10607 ax-bdex 10610 ax-bdeq 10611 ax-bdel 10612 ax-bdsb 10613 ax-bdsep 10675 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-uni 3602 df-bdc 10632 |
This theorem is referenced by: (None) |
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