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Mirrors > Home > ILE Home > Th. List > spc3gv | Unicode version |
Description: Specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.) |
Ref | Expression |
---|---|
spc3egv.1 |
Ref | Expression |
---|---|
spc3gv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2568 | . . . 4 | |
2 | elisset 2568 | . . . 4 | |
3 | elisset 2568 | . . . 4 | |
4 | 1, 2, 3 | 3anim123i 1089 | . . 3 |
5 | eeeanv 1808 | . . 3 | |
6 | 4, 5 | sylibr 137 | . 2 |
7 | spc3egv.1 | . . . . . . . 8 | |
8 | 7 | biimpcd 148 | . . . . . . 7 |
9 | 8 | 2alimi 1345 | . . . . . 6 |
10 | 9 | alimi 1344 | . . . . 5 |
11 | exim 1490 | . . . . . 6 | |
12 | 11 | 2alimi 1345 | . . . . 5 |
13 | 10, 12 | syl 14 | . . . 4 |
14 | exim 1490 | . . . . 5 | |
15 | 14 | alimi 1344 | . . . 4 |
16 | exim 1490 | . . . 4 | |
17 | 13, 15, 16 | 3syl 17 | . . 3 |
18 | 19.9v 1751 | . . . 4 | |
19 | 19.9v 1751 | . . . 4 | |
20 | 19.9v 1751 | . . . 4 | |
21 | 18, 19, 20 | 3bitri 195 | . . 3 |
22 | 17, 21 | syl6ib 150 | . 2 |
23 | 6, 22 | syl5com 26 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 w3a 885 wal 1241 wceq 1243 wex 1381 wcel 1393 |
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: funopg 4934 |
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