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Mirrors > Home > ILE Home > Th. List > ralunb | Unicode version |
Description: Restricted quantification over a union. (Contributed by Scott Fenton, 12-Apr-2011.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
ralunb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elun 3212 | . . . . . 6 | |
2 | 1 | imbi1i 237 | . . . . 5 |
3 | jaob 699 | . . . . 5 | |
4 | 2, 3 | bitri 183 | . . . 4 |
5 | 4 | albii 1446 | . . 3 |
6 | 19.26 1457 | . . 3 | |
7 | 5, 6 | bitri 183 | . 2 |
8 | df-ral 2419 | . 2 | |
9 | df-ral 2419 | . . 3 | |
10 | df-ral 2419 | . . 3 | |
11 | 9, 10 | anbi12i 455 | . 2 |
12 | 7, 8, 11 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 697 wal 1329 wcel 1480 wral 2414 cun 3064 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-un 3070 |
This theorem is referenced by: ralun 3253 ralprg 3569 raltpg 3571 ralunsn 3719 rexfiuz 10754 modfsummodlemstep 11219 modfsummod 11220 zsupcllemstep 11627 prmind2 11790 nninfsellemdc 13195 nninfsellemsuc 13197 |
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