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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 889 | . . . . 5 | |
2 | 1 | exbii 1496 | . . . 4 |
3 | 19.42v 1786 | . . . 4 | |
4 | 2, 3 | bitri 173 | . . 3 |
5 | 4 | exbii 1496 | . 2 |
6 | nfv 1421 | . . . . 5 | |
7 | ceqsex2.1 | . . . . 5 | |
8 | 6, 7 | nfan 1457 | . . . 4 |
9 | 8 | nfex 1528 | . . 3 |
10 | ceqsex2.3 | . . 3 | |
11 | ceqsex2.5 | . . . . 5 | |
12 | 11 | anbi2d 437 | . . . 4 |
13 | 12 | exbidv 1706 | . . 3 |
14 | 9, 10, 13 | ceqsex 2592 | . 2 |
15 | ceqsex2.2 | . . 3 | |
16 | ceqsex2.4 | . . 3 | |
17 | ceqsex2.6 | . . 3 | |
18 | 15, 16, 17 | ceqsex 2592 | . 2 |
19 | 5, 14, 18 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wnf 1349 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: ceqsex2v 2595 |
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