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Mirrors > Home > ILE Home > Th. List > eliun | Unicode version |
Description: Membership in indexed union. (Contributed by NM, 3-Sep-2003.) |
Ref | Expression |
---|---|
eliun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2697 | . 2 | |
2 | elex 2697 | . . 3 | |
3 | 2 | rexlimivw 2545 | . 2 |
4 | eleq1 2202 | . . . 4 | |
5 | 4 | rexbidv 2438 | . . 3 |
6 | df-iun 3815 | . . 3 | |
7 | 5, 6 | elab2g 2831 | . 2 |
8 | 1, 3, 7 | pm5.21nii 693 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1331 wcel 1480 wrex 2417 cvv 2686 ciun 3813 |
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-ral 2421 df-rex 2422 df-v 2688 df-iun 3815 |
This theorem is referenced by: iuncom 3819 iuncom4 3820 iunconstm 3821 iuniin 3823 iunss1 3824 ss2iun 3828 dfiun2g 3845 ssiun 3855 ssiun2 3856 iunab 3859 iun0 3869 0iun 3870 iunn0m 3873 iunin2 3876 iundif2ss 3878 iindif2m 3880 iunxsng 3888 iunxsngf 3890 iunun 3891 iunxun 3892 iunxiun 3894 iunpwss 3904 disjiun 3924 triun 4039 iunpw 4401 xpiundi 4597 xpiundir 4598 iunxpf 4687 cnvuni 4725 dmiun 4748 dmuni 4749 rniun 4949 dfco2 5038 dfco2a 5039 coiun 5048 fun11iun 5388 imaiun 5661 eluniimadm 5666 opabex3d 6019 opabex3 6020 smoiun 6198 tfrlemi14d 6230 tfr1onlemres 6246 tfrcllemres 6259 fsum2dlemstep 11203 fisumcom2 11207 fsumiun 11246 ennnfonelemrn 11932 ennnfonelemdm 11933 ctiunctlemf 11951 ctiunctlemfo 11952 |
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