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Mirrors > Home > ILE Home > Th. List > ceqsex3v | Unicode version |
Description: Elimination of three existential quantifiers, using implicit substitution. (Contributed by NM, 16-Aug-2011.) |
Ref | Expression |
---|---|
ceqsex3v.1 | |
ceqsex3v.2 | |
ceqsex3v.3 | |
ceqsex3v.4 | |
ceqsex3v.5 | |
ceqsex3v.6 |
Ref | Expression |
---|---|
ceqsex3v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 398 | . . . . . 6 | |
2 | 3anass 966 | . . . . . . 7 | |
3 | 2 | anbi1i 453 | . . . . . 6 |
4 | df-3an 964 | . . . . . . 7 | |
5 | 4 | anbi2i 452 | . . . . . 6 |
6 | 1, 3, 5 | 3bitr4i 211 | . . . . 5 |
7 | 6 | 2exbii 1585 | . . . 4 |
8 | 19.42vv 1883 | . . . 4 | |
9 | 7, 8 | bitri 183 | . . 3 |
10 | 9 | exbii 1584 | . 2 |
11 | ceqsex3v.1 | . . . 4 | |
12 | ceqsex3v.4 | . . . . . 6 | |
13 | 12 | 3anbi3d 1296 | . . . . 5 |
14 | 13 | 2exbidv 1840 | . . . 4 |
15 | 11, 14 | ceqsexv 2725 | . . 3 |
16 | ceqsex3v.2 | . . . 4 | |
17 | ceqsex3v.3 | . . . 4 | |
18 | ceqsex3v.5 | . . . 4 | |
19 | ceqsex3v.6 | . . . 4 | |
20 | 16, 17, 18, 19 | ceqsex2v 2727 | . . 3 |
21 | 15, 20 | bitri 183 | . 2 |
22 | 10, 21 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wceq 1331 wex 1468 wcel 1480 cvv 2686 |
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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 |
This theorem is referenced by: ceqsex6v 2730 |
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