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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 2560 |
. 2
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2 | elex 2560 |
. . 3
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3 | 2 | rexlimivw 2423 |
. 2
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4 | eleq1 2097 |
. . . 4
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5 | 4 | rexbidv 2321 |
. . 3
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6 | df-iun 3650 |
. . 3
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7 | 5, 6 | elab2g 2683 |
. 2
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8 | 1, 3, 7 | pm5.21nii 619 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-iun 3650 |
This theorem is referenced by: iuncom 3654 iuncom4 3655 iunconstm 3656 iuniin 3658 iunss1 3659 ss2iun 3663 dfiun2g 3680 ssiun 3690 ssiun2 3691 iunab 3694 iun0 3704 0iun 3705 iunn0m 3708 iunin2 3711 iundif2ss 3713 iindif2m 3715 iunxsng 3723 iunun 3725 iunxun 3726 iunxiun 3727 iunpwss 3734 triun 3858 iunpw 4177 xpiundi 4341 xpiundir 4342 iunxpf 4427 cnvuni 4464 dmiun 4487 dmuni 4488 rniun 4677 dfco2 4763 dfco2a 4764 coiun 4773 fun11iun 5090 imaiun 5342 eluniimadm 5347 opabex3d 5690 opabex3 5691 smoiun 5857 tfrlemi14d 5888 |
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