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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-dfom | Unicode version |
Description: Alternate definition of , as the intersection of all the inductive sets. Proposal: make this the definition. (Contributed by BJ, 30-Nov-2019.) |
Ref | Expression |
---|---|
bj-dfom | Ind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfom3 4563 | . 2 | |
2 | df-bj-ind 13650 | . . . . 5 Ind | |
3 | 2 | bicomi 131 | . . . 4 Ind |
4 | 3 | abbii 2280 | . . 3 Ind |
5 | 4 | inteqi 3822 | . 2 Ind |
6 | 1, 5 | eqtri 2185 | 1 Ind |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1342 wcel 2135 cab 2150 wral 2442 c0 3404 cint 3818 csuc 4337 com 4561 Ind wind 13649 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-int 3819 df-iom 4562 df-bj-ind 13650 |
This theorem is referenced by: bj-omind 13657 bj-omssind 13658 bj-ssom 13659 |
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