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Mirrors > Home > ILE Home > Th. List > spc3egv | Unicode version |
Description: Existential specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.) |
Ref | Expression |
---|---|
spc3egv.1 |
Ref | Expression |
---|---|
spc3egv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2613 | . . . 4 | |
2 | elisset 2613 | . . . 4 | |
3 | elisset 2613 | . . . 4 | |
4 | 1, 2, 3 | 3anim123i 1123 | . . 3 |
5 | eeeanv 1849 | . . 3 | |
6 | 4, 5 | sylibr 132 | . 2 |
7 | spc3egv.1 | . . . . 5 | |
8 | 7 | biimprcd 158 | . . . 4 |
9 | 8 | eximdv 1801 | . . 3 |
10 | 9 | 2eximdv 1803 | . 2 |
11 | 6, 10 | syl5com 29 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 w3a 919 wceq 1284 wex 1421 wcel 1433 |
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) |
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