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Mirrors > Home > ILE Home > Th. List > spc2gv | Unicode version |
Description: Specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 27-Apr-2004.) |
Ref | Expression |
---|---|
spc2egv.1 |
Ref | Expression |
---|---|
spc2gv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2613 | . . . 4 | |
2 | elisset 2613 | . . . 4 | |
3 | 1, 2 | anim12i 331 | . . 3 |
4 | eeanv 1848 | . . 3 | |
5 | 3, 4 | sylibr 132 | . 2 |
6 | spc2egv.1 | . . . . . 6 | |
7 | 6 | biimpcd 157 | . . . . 5 |
8 | 7 | 2alimi 1385 | . . . 4 |
9 | exim 1530 | . . . . 5 | |
10 | 9 | alimi 1384 | . . . 4 |
11 | exim 1530 | . . . 4 | |
12 | 8, 10, 11 | 3syl 17 | . . 3 |
13 | 19.9v 1792 | . . . 4 | |
14 | 19.9v 1792 | . . . 4 | |
15 | 13, 14 | bitri 182 | . . 3 |
16 | 12, 15 | syl6ib 159 | . 2 |
17 | 5, 16 | syl5com 29 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 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-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: rspc2gv 2712 trel 3882 elovmpt2 5721 |
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