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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 2741 | . 2 | |
2 | elex 2741 | . . . 4 | |
3 | 2 | adantr 274 | . . 3 |
4 | 3 | exlimiv 1591 | . 2 |
5 | eleq1 2233 | . . . . 5 | |
6 | 5 | anbi1d 462 | . . . 4 |
7 | 6 | exbidv 1818 | . . 3 |
8 | df-uni 3797 | . . 3 | |
9 | 7, 8 | elab2g 2877 | . 2 |
10 | 1, 4, 9 | pm5.21nii 699 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1348 wex 1485 wcel 2141 cvv 2730 cuni 3796 |
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-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-uni 3797 |
This theorem is referenced by: eluni2 3800 elunii 3801 eluniab 3808 uniun 3815 uniin 3816 uniss 3817 unissb 3826 dftr2 4089 unidif0 4153 unipw 4202 uniex2 4421 uniuni 4436 limom 4598 dmuni 4821 fununi 5266 nfvres 5529 elunirn 5745 tfrlem7 6296 tfrexlem 6313 tfrcldm 6342 fiuni 6955 isbasis2g 12837 tgval2 12845 ntreq0 12926 bj-uniex2 13951 |
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