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Mirrors > Home > ILE Home > Th. List > eluni | Unicode version |
Description: Membership in class union. (Contributed by NM, 22-May-1994.) |
Ref | Expression |
---|---|
eluni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2723 | . 2 | |
2 | elex 2723 | . . . 4 | |
3 | 2 | adantr 274 | . . 3 |
4 | 3 | exlimiv 1578 | . 2 |
5 | eleq1 2220 | . . . . 5 | |
6 | 5 | anbi1d 461 | . . . 4 |
7 | 6 | exbidv 1805 | . . 3 |
8 | df-uni 3773 | . . 3 | |
9 | 7, 8 | elab2g 2859 | . 2 |
10 | 1, 4, 9 | pm5.21nii 694 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1335 wex 1472 wcel 2128 cvv 2712 cuni 3772 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-uni 3773 |
This theorem is referenced by: eluni2 3776 elunii 3777 eluniab 3784 uniun 3791 uniin 3792 uniss 3793 unissb 3802 dftr2 4064 unidif0 4128 unipw 4177 uniex2 4396 uniuni 4411 limom 4573 dmuni 4796 fununi 5238 nfvres 5501 elunirn 5716 tfrlem7 6264 tfrexlem 6281 tfrcldm 6310 fiuni 6922 isbasis2g 12454 tgval2 12462 ntreq0 12543 bj-uniex2 13502 |
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