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Mirrors > Home > ILE Home > Th. List > eluni | Unicode version |
Description: Membership in class union. (Contributed by NM, 22-May-1994.) |
Ref | Expression |
---|---|
eluni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2697 | . 2 | |
2 | elex 2697 | . . . 4 | |
3 | 2 | adantr 274 | . . 3 |
4 | 3 | exlimiv 1577 | . 2 |
5 | eleq1 2202 | . . . . 5 | |
6 | 5 | anbi1d 460 | . . . 4 |
7 | 6 | exbidv 1797 | . . 3 |
8 | df-uni 3737 | . . 3 | |
9 | 7, 8 | elab2g 2831 | . 2 |
10 | 1, 4, 9 | pm5.21nii 693 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 cvv 2686 cuni 3736 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-uni 3737 |
This theorem is referenced by: eluni2 3740 elunii 3741 eluniab 3748 uniun 3755 uniin 3756 uniss 3757 unissb 3766 dftr2 4028 unidif0 4091 unipw 4139 uniex2 4358 uniuni 4372 limom 4527 dmuni 4749 fununi 5191 nfvres 5454 elunirn 5667 tfrlem7 6214 tfrexlem 6231 tfrcldm 6260 fiuni 6866 isbasis2g 12212 tgval2 12220 ntreq0 12301 bj-uniex2 13114 |
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