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Mirrors > Home > ILE Home > Th. List > cbvreuvw | Unicode version |
Description: Version of cbvreuv 2691 with a disjoint variable condition. (Contributed by Gino Giotto, 10-Jan-2024.) Reduce axiom usage. (Revised by Gino Giotto, 25-Aug-2024.) |
Ref | Expression |
---|---|
cbvralvw.1 |
Ref | Expression |
---|---|
cbvreuvw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1w 2225 | . . . . . . 7 | |
2 | cbvralvw.1 | . . . . . . 7 | |
3 | 1, 2 | anbi12d 465 | . . . . . 6 |
4 | equequ1 1699 | . . . . . 6 | |
5 | 3, 4 | bibi12d 234 | . . . . 5 |
6 | 5 | cbvalvw 1906 | . . . 4 |
7 | 6 | exbii 1592 | . . 3 |
8 | df-eu 2016 | . . 3 | |
9 | df-eu 2016 | . . 3 | |
10 | 7, 8, 9 | 3bitr4ri 212 | . 2 |
11 | df-reu 2449 | . 2 | |
12 | df-reu 2449 | . 2 | |
13 | 10, 11, 12 | 3bitr4ri 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wex 1479 weu 2013 wcel 2135 wreu 2444 |
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-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 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-eu 2016 df-clel 2160 df-reu 2449 |
This theorem is referenced by: (None) |
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