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Mirrors > Home > ILE Home > Th. List > cgsex2g | Unicode version |
Description: Implicit substitution inference for general classes. (Contributed by NM, 26-Jul-1995.) |
Ref | Expression |
---|---|
cgsex2g.1 | |
cgsex2g.2 |
Ref | Expression |
---|---|
cgsex2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cgsex2g.2 | . . . 4 | |
2 | 1 | biimpa 280 | . . 3 |
3 | 2 | exlimivv 1776 | . 2 |
4 | elisset 2568 | . . . . . 6 | |
5 | elisset 2568 | . . . . . 6 | |
6 | 4, 5 | anim12i 321 | . . . . 5 |
7 | eeanv 1807 | . . . . 5 | |
8 | 6, 7 | sylibr 137 | . . . 4 |
9 | cgsex2g.1 | . . . . 5 | |
10 | 9 | 2eximi 1492 | . . . 4 |
11 | 8, 10 | syl 14 | . . 3 |
12 | 1 | biimprcd 149 | . . . . 5 |
13 | 12 | ancld 308 | . . . 4 |
14 | 13 | 2eximdv 1762 | . . 3 |
15 | 11, 14 | syl5com 26 | . 2 |
16 | 3, 15 | impbid2 131 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 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: (None) |
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