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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 3589 | . . 3 |
3 | 2 | ralbidv 2368 | . 2 |
4 | 2ralunsn.1 | . . . . . 6 | |
5 | 4 | ralbidv 2368 | . . . . 5 |
6 | 2ralunsn.3 | . . . . 5 | |
7 | 5, 6 | anbi12d 456 | . . . 4 |
8 | 7 | ralunsn 3589 | . . 3 |
9 | r19.26 2485 | . . . 4 | |
10 | 9 | anbi1i 445 | . . 3 |
11 | 8, 10 | syl6bb 194 | . 2 |
12 | 3, 11 | bitrd 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wcel 1433 wral 2348 cun 2971 csn 3398 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-sbc 2816 df-un 2977 df-sn 3404 |
This theorem is referenced by: (None) |
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