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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 2267 |
. . 3
| |
| 2 | 1 | ralbidv 2505 |
. 2
|
| 3 | df-iin 3929 |
. 2
| |
| 4 | 2, 3 | elab2g 2919 |
1
|
| 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 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-tru 1375 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-ral 2488 df-v 2773 df-iin 3929 |
| This theorem is referenced by: iinconstm 3935 iuniin 3936 iinss1 3938 ssiinf 3976 iinss 3978 iinss2 3979 iinab 3988 iundif2ss 3992 iindif2m 3994 iinin2m 3995 elriin 3997 iinpw 4017 xpiindim 4814 cnviinm 5223 iinerm 6693 ixpiinm 6810 |
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