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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2748 |
. 2
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2 | elex 2748 |
. . . 4
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3 | 2 | adantr 276 |
. . 3
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4 | 3 | exlimiv 1598 |
. 2
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5 | eleq1 2240 |
. . . . 5
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6 | 5 | anbi1d 465 |
. . . 4
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7 | 6 | exbidv 1825 |
. . 3
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8 | df-uni 3810 |
. . 3
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9 | 7, 8 | elab2g 2884 |
. 2
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10 | 1, 4, 9 | 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-v 2739 df-uni 3810 |
This theorem is referenced by: eluni2 3813 elunii 3814 eluniab 3821 uniun 3828 uniin 3829 uniss 3830 unissb 3839 dftr2 4103 unidif0 4167 unipw 4217 uniex2 4436 uniuni 4451 limom 4613 dmuni 4837 fununi 5284 nfvres 5548 elunirn 5766 tfrlem7 6317 tfrexlem 6334 tfrcldm 6363 fiuni 6976 isbasis2g 13436 tgval2 13444 ntreq0 13525 bj-uniex2 14550 |
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