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Mirrors > Home > NFE 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 2413 | . . 3 | |
2 | 1 | ralbidv 2634 | . 2 |
3 | df-iin 3972 | . 2 | |
4 | 2, 3 | elab2g 2987 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wceq 1642 wcel 1710 wral 2614 ciin 3970 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-v 2861 df-iin 3972 |
This theorem is referenced by: iinconst 3978 iuniin 3979 iinss1 3981 ssiinf 4015 iinss 4017 iinss2 4018 iinab 4027 iinun2 4032 iundif2 4033 iindif2 4035 iinin2 4036 elriin 4038 iinxprg 4043 iinuni 4049 iinpw 4054 cnviin 5118 |
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