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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-indeq | Unicode version |
Description: Equality property for Ind. (Contributed by BJ, 30-Nov-2019.) |
Ref | Expression |
---|---|
bj-indeq | Ind Ind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2234 | . . 3 | |
2 | eleq2 2234 | . . . 4 | |
3 | 2 | raleqbi1dv 2673 | . . 3 |
4 | 1, 3 | anbi12d 470 | . 2 |
5 | df-bj-ind 13884 | . 2 Ind | |
6 | df-bj-ind 13884 | . 2 Ind | |
7 | 4, 5, 6 | 3bitr4g 222 | 1 Ind Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 wral 2448 c0 3414 csuc 4348 Ind wind 13883 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-bj-ind 13884 |
This theorem is referenced by: bj-omind 13891 bj-omssind 13892 bj-ssom 13893 bj-om 13894 bj-2inf 13895 |
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