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Mirrors > Home > NFE 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 470 | . . . 4 |
3 | 2 | exlimivv 1635 | . . 3 |
4 | 3 | exlimivv 1635 | . 2 |
5 | elisset 2869 | . . . . . . . 8 | |
6 | elisset 2869 | . . . . . . . 8 | |
7 | 5, 6 | anim12i 549 | . . . . . . 7 |
8 | eeanv 1913 | . . . . . . 7 | |
9 | 7, 8 | sylibr 203 | . . . . . 6 |
10 | elisset 2869 | . . . . . . . 8 | |
11 | elisset 2869 | . . . . . . . 8 | |
12 | 10, 11 | anim12i 549 | . . . . . . 7 |
13 | eeanv 1913 | . . . . . . 7 | |
14 | 12, 13 | sylibr 203 | . . . . . 6 |
15 | 9, 14 | anim12i 549 | . . . . 5 |
16 | ee4anv 1915 | . . . . 5 | |
17 | 15, 16 | sylibr 203 | . . . 4 |
18 | cgsex4g.1 | . . . . . 6 | |
19 | 18 | 2eximi 1577 | . . . . 5 |
20 | 19 | 2eximi 1577 | . . . 4 |
21 | 17, 20 | syl 15 | . . 3 |
22 | 1 | biimprcd 216 | . . . . . 6 |
23 | 22 | ancld 536 | . . . . 5 |
24 | 23 | 2eximdv 1624 | . . . 4 |
25 | 24 | 2eximdv 1624 | . . 3 |
26 | 21, 25 | syl5com 26 | . 2 |
27 | 4, 26 | impbid2 195 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wceq 1642 wcel 1710 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2861 |
This theorem is referenced by: copsex4g 4610 |
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