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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-uniex2 | Unicode version |
Description: uniex2 4328 from bounded separation. (Contributed by BJ, 15-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-uniex2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcuni 13001 | . . . 4 BOUNDED | |
2 | 1 | bdeli 12971 | . . 3 BOUNDED |
3 | zfun 4326 | . . . 4 | |
4 | eluni 3709 | . . . . . . 7 | |
5 | 4 | imbi1i 237 | . . . . . 6 |
6 | 5 | albii 1431 | . . . . 5 |
7 | 6 | exbii 1569 | . . . 4 |
8 | 3, 7 | mpbir 145 | . . 3 |
9 | 2, 8 | bdbm1.3ii 13016 | . 2 |
10 | dfcleq 2111 | . . 3 | |
11 | 10 | exbii 1569 | . 2 |
12 | 9, 11 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wceq 1316 wex 1453 wcel 1465 cuni 3706 |
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-un 4325 ax-bd0 12938 ax-bdex 12944 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-uni 3707 df-bdc 12966 |
This theorem is referenced by: bj-uniex 13042 |
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