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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2252 |
. . 3
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2 | 1 | ralbidv 2490 |
. 2
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3 | df-iin 3904 |
. 2
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4 | 2, 3 | elab2g 2899 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-v 2754 df-iin 3904 |
This theorem is referenced by: iinconstm 3910 iuniin 3911 iinss1 3913 ssiinf 3951 iinss 3953 iinss2 3954 iinab 3963 iundif2ss 3967 iindif2m 3969 iinin2m 3970 elriin 3972 iinpw 3992 xpiindim 4782 cnviinm 5188 iinerm 6632 ixpiinm 6749 |
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