Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ceqsex8v | Unicode version |
Description: Elimination of eight existential quantifiers, using implicit substitution. (Contributed by NM, 23-Sep-2011.) |
Ref | Expression |
---|---|
ceqsex8v.1 | |
ceqsex8v.2 | |
ceqsex8v.3 | |
ceqsex8v.4 | |
ceqsex8v.5 | |
ceqsex8v.6 | |
ceqsex8v.7 | |
ceqsex8v.8 | |
ceqsex8v.9 | |
ceqsex8v.10 | |
ceqsex8v.11 | |
ceqsex8v.12 | |
ceqsex8v.13 | |
ceqsex8v.14 | |
ceqsex8v.15 | |
ceqsex8v.16 |
Ref | Expression |
---|---|
ceqsex8v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.42vvvv 1831 | . . . . 5 | |
2 | 3anass 923 | . . . . . . . 8 | |
3 | df-3an 921 | . . . . . . . . 9 | |
4 | 3 | anbi2i 444 | . . . . . . . 8 |
5 | 2, 4 | bitr4i 185 | . . . . . . 7 |
6 | 5 | 2exbii 1537 | . . . . . 6 |
7 | 6 | 2exbii 1537 | . . . . 5 |
8 | df-3an 921 | . . . . 5 | |
9 | 1, 7, 8 | 3bitr4i 210 | . . . 4 |
10 | 9 | 2exbii 1537 | . . 3 |
11 | 10 | 2exbii 1537 | . 2 |
12 | ceqsex8v.1 | . . . 4 | |
13 | ceqsex8v.2 | . . . 4 | |
14 | ceqsex8v.3 | . . . 4 | |
15 | ceqsex8v.4 | . . . 4 | |
16 | ceqsex8v.9 | . . . . . 6 | |
17 | 16 | 3anbi3d 1249 | . . . . 5 |
18 | 17 | 4exbidv 1791 | . . . 4 |
19 | ceqsex8v.10 | . . . . . 6 | |
20 | 19 | 3anbi3d 1249 | . . . . 5 |
21 | 20 | 4exbidv 1791 | . . . 4 |
22 | ceqsex8v.11 | . . . . . 6 | |
23 | 22 | 3anbi3d 1249 | . . . . 5 |
24 | 23 | 4exbidv 1791 | . . . 4 |
25 | ceqsex8v.12 | . . . . . 6 | |
26 | 25 | 3anbi3d 1249 | . . . . 5 |
27 | 26 | 4exbidv 1791 | . . . 4 |
28 | 12, 13, 14, 15, 18, 21, 24, 27 | ceqsex4v 2642 | . . 3 |
29 | ceqsex8v.5 | . . . 4 | |
30 | ceqsex8v.6 | . . . 4 | |
31 | ceqsex8v.7 | . . . 4 | |
32 | ceqsex8v.8 | . . . 4 | |
33 | ceqsex8v.13 | . . . 4 | |
34 | ceqsex8v.14 | . . . 4 | |
35 | ceqsex8v.15 | . . . 4 | |
36 | ceqsex8v.16 | . . . 4 | |
37 | 29, 30, 31, 32, 33, 34, 35, 36 | ceqsex4v 2642 | . . 3 |
38 | 28, 37 | bitri 182 | . 2 |
39 | 11, 38 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wceq 1284 wex 1421 wcel 1433 cvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |