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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdunexb | Unicode version |
Description: Bounded version of unexb 4333. (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 3193 | . . . 4 | |
2 | 1 | eleq1d 2186 | . . 3 |
3 | uneq2 3194 | . . . 4 | |
4 | 3 | eleq1d 2186 | . . 3 |
5 | vex 2663 | . . . 4 | |
6 | vex 2663 | . . . 4 | |
7 | 5, 6 | bj-unex 13044 | . . 3 |
8 | 2, 4, 7 | vtocl2g 2724 | . 2 |
9 | ssun1 3209 | . . . 4 | |
10 | bdunex.bd1 | . . . . 5 BOUNDED | |
11 | 10 | bdssexg 13029 | . . . 4 |
12 | 9, 11 | mpan 420 | . . 3 |
13 | ssun2 3210 | . . . 4 | |
14 | bdunex.bd2 | . . . . 5 BOUNDED | |
15 | 14 | bdssexg 13029 | . . . 4 |
16 | 13, 15 | mpan 420 | . . 3 |
17 | 12, 16 | jca 304 | . 2 |
18 | 8, 17 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1316 wcel 1465 cvv 2660 cun 3039 wss 3041 BOUNDED wbdc 12965 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-pr 4101 ax-un 4325 ax-bd0 12938 ax-bdor 12941 ax-bdex 12944 ax-bdeq 12945 ax-bdel 12946 ax-bdsb 12947 ax-bdsep 13009 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-uni 3707 df-bdc 12966 |
This theorem is referenced by: (None) |
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