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Mirrors > Home > ILE Home > Th. List > ceqsex6v | Unicode version |
Description: Elimination of six existential quantifiers, using implicit substitution. (Contributed by NM, 21-Sep-2011.) |
Ref | Expression |
---|---|
ceqsex6v.1 | |
ceqsex6v.2 | |
ceqsex6v.3 | |
ceqsex6v.4 | |
ceqsex6v.5 | |
ceqsex6v.6 | |
ceqsex6v.7 | |
ceqsex6v.8 | |
ceqsex6v.9 | |
ceqsex6v.10 | |
ceqsex6v.11 | |
ceqsex6v.12 |
Ref | Expression |
---|---|
ceqsex6v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anass 971 | . . . . 5 | |
2 | 1 | 3exbii 1594 | . . . 4 |
3 | 19.42vvv 1899 | . . . 4 | |
4 | 2, 3 | bitri 183 | . . 3 |
5 | 4 | 3exbii 1594 | . 2 |
6 | ceqsex6v.1 | . . . 4 | |
7 | ceqsex6v.2 | . . . 4 | |
8 | ceqsex6v.3 | . . . 4 | |
9 | ceqsex6v.7 | . . . . . 6 | |
10 | 9 | anbi2d 460 | . . . . 5 |
11 | 10 | 3exbidv 1856 | . . . 4 |
12 | ceqsex6v.8 | . . . . . 6 | |
13 | 12 | anbi2d 460 | . . . . 5 |
14 | 13 | 3exbidv 1856 | . . . 4 |
15 | ceqsex6v.9 | . . . . . 6 | |
16 | 15 | anbi2d 460 | . . . . 5 |
17 | 16 | 3exbidv 1856 | . . . 4 |
18 | 6, 7, 8, 11, 14, 17 | ceqsex3v 2766 | . . 3 |
19 | ceqsex6v.4 | . . . 4 | |
20 | ceqsex6v.5 | . . . 4 | |
21 | ceqsex6v.6 | . . . 4 | |
22 | ceqsex6v.10 | . . . 4 | |
23 | ceqsex6v.11 | . . . 4 | |
24 | ceqsex6v.12 | . . . 4 | |
25 | 19, 20, 21, 22, 23, 24 | ceqsex3v 2766 | . . 3 |
26 | 18, 25 | bitri 183 | . 2 |
27 | 5, 26 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 967 wceq 1342 wex 1479 wcel 2135 cvv 2724 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-v 2726 |
This theorem is referenced by: (None) |
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