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Mirrors > Home > ILE Home > Th. List > 2ralunsn | Unicode version |
Description: Double restricted quantification over the union of a set and a singleton, using implicit substitution. (Contributed by Paul Chapman, 17-Nov-2012.) |
Ref | Expression |
---|---|
2ralunsn.1 | |
2ralunsn.2 | |
2ralunsn.3 |
Ref | Expression |
---|---|
2ralunsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2ralunsn.2 | . . . 4 | |
2 | 1 | ralunsn 3568 | . . 3 |
3 | 2 | ralbidv 2326 | . 2 |
4 | 2ralunsn.1 | . . . . . 6 | |
5 | 4 | ralbidv 2326 | . . . . 5 |
6 | 2ralunsn.3 | . . . . 5 | |
7 | 5, 6 | anbi12d 442 | . . . 4 |
8 | 7 | ralunsn 3568 | . . 3 |
9 | r19.26 2441 | . . . 4 | |
10 | 9 | anbi1i 431 | . . 3 |
11 | 8, 10 | syl6bb 185 | . 2 |
12 | 3, 11 | bitrd 177 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 wral 2306 cun 2915 csn 3375 |
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-3an 887 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-sbc 2765 df-un 2922 df-sn 3381 |
This theorem is referenced by: (None) |
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