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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 3084 | . . . . . 6 | |
2 | 1 | imbi1i 227 | . . . . 5 |
3 | jaob 631 | . . . . 5 | |
4 | 2, 3 | bitri 173 | . . . 4 |
5 | 4 | albii 1359 | . . 3 |
6 | 19.26 1370 | . . 3 | |
7 | 5, 6 | bitri 173 | . 2 |
8 | df-ral 2311 | . 2 | |
9 | df-ral 2311 | . . 3 | |
10 | df-ral 2311 | . . 3 | |
11 | 9, 10 | anbi12i 433 | . 2 |
12 | 7, 8, 11 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wo 629 wal 1241 wcel 1393 wral 2306 cun 2915 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-un 2922 |
This theorem is referenced by: ralun 3125 ralprg 3421 raltpg 3423 ralunsn 3568 |
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