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Mirrors > Home > ILE Home > Th. List > ceqsex2 | Unicode version |
Description: Elimination of two existential quantifiers, using implicit substitution. (Contributed by Scott Fenton, 7-Jun-2006.) |
Ref | Expression |
---|---|
ceqsex2.1 | |
ceqsex2.2 | |
ceqsex2.3 | |
ceqsex2.4 | |
ceqsex2.5 | |
ceqsex2.6 |
Ref | Expression |
---|---|
ceqsex2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anass 971 | . . . . 5 | |
2 | 1 | exbii 1592 | . . . 4 |
3 | 19.42v 1893 | . . . 4 | |
4 | 2, 3 | bitri 183 | . . 3 |
5 | 4 | exbii 1592 | . 2 |
6 | nfv 1515 | . . . . 5 | |
7 | ceqsex2.1 | . . . . 5 | |
8 | 6, 7 | nfan 1552 | . . . 4 |
9 | 8 | nfex 1624 | . . 3 |
10 | ceqsex2.3 | . . 3 | |
11 | ceqsex2.5 | . . . . 5 | |
12 | 11 | anbi2d 460 | . . . 4 |
13 | 12 | exbidv 1812 | . . 3 |
14 | 9, 10, 13 | ceqsex 2759 | . 2 |
15 | ceqsex2.2 | . . 3 | |
16 | ceqsex2.4 | . . 3 | |
17 | ceqsex2.6 | . . 3 | |
18 | 15, 16, 17 | ceqsex 2759 | . 2 |
19 | 5, 14, 18 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 967 wceq 1342 wnf 1447 wex 1479 wcel 2135 cvv 2721 |
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 2723 |
This theorem is referenced by: ceqsex2v 2762 |
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