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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nalset | Unicode version |
Description: nalset 4107 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nalset |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alexnim 1635 | . 2 | |
2 | ax-bdel 13555 | . . . . 5 BOUNDED | |
3 | 2 | ax-bdn 13551 | . . . 4 BOUNDED |
4 | 3 | bdsep1 13619 | . . 3 |
5 | elequ1 2139 | . . . . . 6 | |
6 | elequ1 2139 | . . . . . . 7 | |
7 | elequ1 2139 | . . . . . . . . 9 | |
8 | elequ2 2140 | . . . . . . . . 9 | |
9 | 7, 8 | bitrd 187 | . . . . . . . 8 |
10 | 9 | notbid 657 | . . . . . . 7 |
11 | 6, 10 | anbi12d 465 | . . . . . 6 |
12 | 5, 11 | bibi12d 234 | . . . . 5 |
13 | 12 | spv 1847 | . . . 4 |
14 | pclem6 1363 | . . . 4 | |
15 | 13, 14 | syl 14 | . . 3 |
16 | 4, 15 | eximii 1589 | . 2 |
17 | 1, 16 | mpg 1438 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wb 104 wal 1340 wex 1479 |
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-in1 604 ax-in2 605 ax-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-13 2137 ax-14 2138 ax-bdn 13551 ax-bdel 13555 ax-bdsep 13618 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 |
This theorem is referenced by: bj-vprc 13630 |
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