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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 381 | . . . . . 6 | |
2 | 3anass 889 | . . . . . . 7 | |
3 | 2 | anbi1i 431 | . . . . . 6 |
4 | df-3an 887 | . . . . . . 7 | |
5 | 4 | anbi2i 430 | . . . . . 6 |
6 | 1, 3, 5 | 3bitr4i 201 | . . . . 5 |
7 | 6 | 2exbii 1497 | . . . 4 |
8 | 19.42vv 1788 | . . . 4 | |
9 | 7, 8 | bitri 173 | . . 3 |
10 | 9 | exbii 1496 | . 2 |
11 | ceqsex3v.1 | . . . 4 | |
12 | ceqsex3v.4 | . . . . . 6 | |
13 | 12 | 3anbi3d 1213 | . . . . 5 |
14 | 13 | 2exbidv 1748 | . . . 4 |
15 | 11, 14 | ceqsexv 2593 | . . 3 |
16 | ceqsex3v.2 | . . . 4 | |
17 | ceqsex3v.3 | . . . 4 | |
18 | ceqsex3v.5 | . . . 4 | |
19 | ceqsex3v.6 | . . . 4 | |
20 | 16, 17, 18, 19 | ceqsex2v 2595 | . . 3 |
21 | 15, 20 | bitri 173 | . 2 |
22 | 10, 21 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wex 1381 wcel 1393 cvv 2557 |
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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: ceqsex6v 2598 |
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