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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 2748 |
. 2
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2 | elex 2748 |
. . 3
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3 | 2 | rexlimivw 2590 |
. 2
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4 | eleq1 2240 |
. . . 4
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5 | 4 | rexbidv 2478 |
. . 3
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6 | df-iun 3888 |
. . 3
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7 | 5, 6 | elab2g 2884 |
. 2
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8 | 1, 3, 7 | pm5.21nii 704 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-iun 3888 |
This theorem is referenced by: iuncom 3892 iuncom4 3893 iunconstm 3894 iuniin 3896 iunss1 3897 ss2iun 3901 dfiun2g 3918 ssiun 3928 ssiun2 3929 iunab 3933 iun0 3943 0iun 3944 iunn0m 3947 iunin2 3950 iundif2ss 3952 iindif2m 3954 iunxsng 3962 iunxsngf 3964 iunun 3965 iunxun 3966 iunxiun 3968 iunpwss 3978 disjiun 3998 triun 4114 iunpw 4480 xpiundi 4684 xpiundir 4685 iunxpf 4775 cnvuni 4813 dmiun 4836 dmuni 4837 rniun 5039 dfco2 5128 dfco2a 5129 coiun 5138 fun11iun 5482 imaiun 5760 eluniimadm 5765 opabex3d 6121 opabex3 6122 smoiun 6301 tfrlemi14d 6333 tfr1onlemres 6349 tfrcllemres 6362 fsum2dlemstep 11441 fisumcom2 11445 fsumiun 11484 fprod2dlemstep 11629 fprodcom2fi 11633 ennnfonelemrn 12419 ennnfonelemdm 12420 ctiunctlemf 12438 ctiunctlemfo 12439 imasaddfnlemg 12734 |
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