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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 2695 | . . . 4 | |
2 | elisset 2695 | . . . 4 | |
3 | elisset 2695 | . . . 4 | |
4 | 1, 2, 3 | 3anim123i 1166 | . . 3 |
5 | eeeanv 1903 | . . 3 | |
6 | 4, 5 | sylibr 133 | . 2 |
7 | spc3egv.1 | . . . . . . . 8 | |
8 | 7 | biimpcd 158 | . . . . . . 7 |
9 | 8 | 2alimi 1432 | . . . . . 6 |
10 | 9 | alimi 1431 | . . . . 5 |
11 | exim 1578 | . . . . . 6 | |
12 | 11 | 2alimi 1432 | . . . . 5 |
13 | 10, 12 | syl 14 | . . . 4 |
14 | exim 1578 | . . . . 5 | |
15 | 14 | alimi 1431 | . . . 4 |
16 | exim 1578 | . . . 4 | |
17 | 13, 15, 16 | 3syl 17 | . . 3 |
18 | 19.9v 1843 | . . . 4 | |
19 | 19.9v 1843 | . . . 4 | |
20 | 19.9v 1843 | . . . 4 | |
21 | 18, 19, 20 | 3bitri 205 | . . 3 |
22 | 17, 21 | syl6ib 160 | . 2 |
23 | 6, 22 | syl5com 29 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 962 wal 1329 wceq 1331 wex 1468 wcel 1480 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 |
This theorem is referenced by: funopg 5152 |
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