Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eliun | Unicode version |
Description: Membership in indexed union. (Contributed by NM, 3-Sep-2003.) |
Ref | Expression |
---|---|
eliun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2671 | . 2 | |
2 | elex 2671 | . . 3 | |
3 | 2 | rexlimivw 2522 | . 2 |
4 | eleq1 2180 | . . . 4 | |
5 | 4 | rexbidv 2415 | . . 3 |
6 | df-iun 3785 | . . 3 | |
7 | 5, 6 | elab2g 2804 | . 2 |
8 | 1, 3, 7 | pm5.21nii 678 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1316 wcel 1465 wrex 2394 cvv 2660 ciun 3783 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-iun 3785 |
This theorem is referenced by: iuncom 3789 iuncom4 3790 iunconstm 3791 iuniin 3793 iunss1 3794 ss2iun 3798 dfiun2g 3815 ssiun 3825 ssiun2 3826 iunab 3829 iun0 3839 0iun 3840 iunn0m 3843 iunin2 3846 iundif2ss 3848 iindif2m 3850 iunxsng 3858 iunxsngf 3860 iunun 3861 iunxun 3862 iunxiun 3864 iunpwss 3874 disjiun 3894 triun 4009 iunpw 4371 xpiundi 4567 xpiundir 4568 iunxpf 4657 cnvuni 4695 dmiun 4718 dmuni 4719 rniun 4919 dfco2 5008 dfco2a 5009 coiun 5018 fun11iun 5356 imaiun 5629 eluniimadm 5634 opabex3d 5987 opabex3 5988 smoiun 6166 tfrlemi14d 6198 tfr1onlemres 6214 tfrcllemres 6227 fsum2dlemstep 11158 fisumcom2 11162 fsumiun 11201 ennnfonelemrn 11843 ennnfonelemdm 11844 ctiunctlemf 11862 ctiunctlemfo 11863 |
Copyright terms: Public domain | W3C validator |