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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2700 |
. 2
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2 | elex 2700 |
. . 3
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3 | 2 | rexlimivw 2548 |
. 2
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4 | eleq1 2203 |
. . . 4
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5 | 4 | rexbidv 2439 |
. . 3
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6 | df-iun 3823 |
. . 3
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7 | 5, 6 | elab2g 2835 |
. 2
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8 | 1, 3, 7 | pm5.21nii 694 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-iun 3823 |
This theorem is referenced by: iuncom 3827 iuncom4 3828 iunconstm 3829 iuniin 3831 iunss1 3832 ss2iun 3836 dfiun2g 3853 ssiun 3863 ssiun2 3864 iunab 3867 iun0 3877 0iun 3878 iunn0m 3881 iunin2 3884 iundif2ss 3886 iindif2m 3888 iunxsng 3896 iunxsngf 3898 iunun 3899 iunxun 3900 iunxiun 3902 iunpwss 3912 disjiun 3932 triun 4047 iunpw 4409 xpiundi 4605 xpiundir 4606 iunxpf 4695 cnvuni 4733 dmiun 4756 dmuni 4757 rniun 4957 dfco2 5046 dfco2a 5047 coiun 5056 fun11iun 5396 imaiun 5669 eluniimadm 5674 opabex3d 6027 opabex3 6028 smoiun 6206 tfrlemi14d 6238 tfr1onlemres 6254 tfrcllemres 6267 fsum2dlemstep 11235 fisumcom2 11239 fsumiun 11278 ennnfonelemrn 11968 ennnfonelemdm 11969 ctiunctlemf 11987 ctiunctlemfo 11988 |
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