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Mirrors > Home > ILE Home > Th. List > eluniab | Unicode version |
Description: Membership in union of a class abstraction. (Contributed by NM, 11-Aug-1994.) (Revised by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
eluniab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluni 3797 | . 2 | |
2 | nfv 1521 | . . . 4 | |
3 | nfsab1 2160 | . . . 4 | |
4 | 2, 3 | nfan 1558 | . . 3 |
5 | nfv 1521 | . . 3 | |
6 | eleq2 2234 | . . . 4 | |
7 | eleq1 2233 | . . . . 5 | |
8 | abid 2158 | . . . . 5 | |
9 | 7, 8 | bitrdi 195 | . . . 4 |
10 | 6, 9 | anbi12d 470 | . . 3 |
11 | 4, 5, 10 | cbvex 1749 | . 2 |
12 | 1, 11 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wex 1485 wcel 2141 cab 2156 cuni 3794 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-uni 3795 |
This theorem is referenced by: elunirab 3807 dfiun2g 3903 inuni 4139 snnex 4431 eliota 5184 elfv 5492 unielxp 6150 tfrlem9 6295 tfr0dm 6298 metrest 13259 |
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