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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 2568 | . . . 4 | |
2 | elisset 2568 | . . . 4 | |
3 | 1, 2 | anim12i 321 | . . 3 |
4 | eeanv 1807 | . . 3 | |
5 | 3, 4 | sylibr 137 | . 2 |
6 | spc2egv.1 | . . . . . 6 | |
7 | 6 | biimpcd 148 | . . . . 5 |
8 | 7 | 2alimi 1345 | . . . 4 |
9 | exim 1490 | . . . . 5 | |
10 | 9 | alimi 1344 | . . . 4 |
11 | exim 1490 | . . . 4 | |
12 | 8, 10, 11 | 3syl 17 | . . 3 |
13 | 19.9v 1751 | . . . 4 | |
14 | 19.9v 1751 | . . . 4 | |
15 | 13, 14 | bitri 173 | . . 3 |
16 | 12, 15 | syl6ib 150 | . 2 |
17 | 5, 16 | syl5com 26 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 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-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: trel 3861 elovmpt2 5701 |
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