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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 3724 | . . 3 |
3 | 2 | ralbidv 2437 | . 2 |
4 | 2ralunsn.1 | . . . . . 6 | |
5 | 4 | ralbidv 2437 | . . . . 5 |
6 | 2ralunsn.3 | . . . . 5 | |
7 | 5, 6 | anbi12d 464 | . . . 4 |
8 | 7 | ralunsn 3724 | . . 3 |
9 | r19.26 2558 | . . . 4 | |
10 | 9 | anbi1i 453 | . . 3 |
11 | 8, 10 | syl6bb 195 | . 2 |
12 | 3, 11 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wral 2416 cun 3069 csn 3527 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-v 2688 df-sbc 2910 df-un 3075 df-sn 3533 |
This theorem is referenced by: (None) |
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