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Mirrors > Home > ILE Home > Th. List > eliin | Unicode version |
Description: Membership in indexed intersection. (Contributed by NM, 3-Sep-2003.) |
Ref | Expression |
---|---|
eliin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2100 | . . 3 | |
2 | 1 | ralbidv 2326 | . 2 |
3 | df-iin 3660 | . 2 | |
4 | 2, 3 | elab2g 2689 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 wral 2306 ciin 3658 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-iin 3660 |
This theorem is referenced by: iinconstm 3666 iuniin 3667 iinss1 3669 ssiinf 3706 iinss 3708 iinss2 3709 iinab 3718 iundif2ss 3722 iindif2m 3724 iinin2m 3725 elriin 3727 iinpw 3742 xpiindim 4473 cnviinm 4859 iinerm 6178 |
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