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Mirrors > Home > ILE Home > Th. List > cgsex4g | Unicode version |
Description: An implicit substitution inference for 4 general classes. (Contributed by NM, 5-Aug-1995.) |
Ref | Expression |
---|---|
cgsex4g.1 | |
cgsex4g.2 |
Ref | Expression |
---|---|
cgsex4g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cgsex4g.2 | . . . . 5 | |
2 | 1 | biimpa 294 | . . . 4 |
3 | 2 | exlimivv 1883 | . . 3 |
4 | 3 | exlimivv 1883 | . 2 |
5 | elisset 2738 | . . . . . . . 8 | |
6 | elisset 2738 | . . . . . . . 8 | |
7 | 5, 6 | anim12i 336 | . . . . . . 7 |
8 | eeanv 1919 | . . . . . . 7 | |
9 | 7, 8 | sylibr 133 | . . . . . 6 |
10 | elisset 2738 | . . . . . . . 8 | |
11 | elisset 2738 | . . . . . . . 8 | |
12 | 10, 11 | anim12i 336 | . . . . . . 7 |
13 | eeanv 1919 | . . . . . . 7 | |
14 | 12, 13 | sylibr 133 | . . . . . 6 |
15 | 9, 14 | anim12i 336 | . . . . 5 |
16 | ee4anv 1921 | . . . . 5 | |
17 | 15, 16 | sylibr 133 | . . . 4 |
18 | cgsex4g.1 | . . . . . 6 | |
19 | 18 | 2eximi 1588 | . . . . 5 |
20 | 19 | 2eximi 1588 | . . . 4 |
21 | 17, 20 | syl 14 | . . 3 |
22 | 1 | biimprcd 159 | . . . . . 6 |
23 | 22 | ancld 323 | . . . . 5 |
24 | 23 | 2eximdv 1869 | . . . 4 |
25 | 24 | 2eximdv 1869 | . . 3 |
26 | 21, 25 | syl5com 29 | . 2 |
27 | 4, 26 | impbid2 142 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wex 1479 wcel 2135 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-v 2726 |
This theorem is referenced by: copsex4g 4222 brecop 6585 |
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