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Mirrors > Home > ILE Home > Th. List > eluni2 | Unicode version |
Description: Membership in class union. Restricted quantifier version. (Contributed by NM, 31-Aug-1999.) |
Ref | Expression |
---|---|
eluni2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exancom 1588 | . 2 | |
2 | eluni 3776 | . 2 | |
3 | df-rex 2441 | . 2 | |
4 | 1, 2, 3 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wex 1472 wcel 2128 wrex 2436 cuni 3773 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-uni 3774 |
This theorem is referenced by: uni0b 3798 intssunim 3830 iuncom4 3857 inuni 4117 ssorduni 4447 unon 4471 cnvuni 4773 chfnrn 5579 isbasis3g 12486 eltg2b 12496 tgcl 12506 epttop 12532 txuni2 12698 |
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