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Mirrors > Home > MPE Home > Th. List > cgsex4g | Structured version Visualization version 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 501 | . . . 4 |
3 | 2 | exlimivv 1860 | . . 3 |
4 | 3 | exlimivv 1860 | . 2 |
5 | elisset 3215 | . . . . . . . 8 | |
6 | elisset 3215 | . . . . . . . 8 | |
7 | 5, 6 | anim12i 590 | . . . . . . 7 |
8 | eeanv 2182 | . . . . . . 7 | |
9 | 7, 8 | sylibr 224 | . . . . . 6 |
10 | elisset 3215 | . . . . . . . 8 | |
11 | elisset 3215 | . . . . . . . 8 | |
12 | 10, 11 | anim12i 590 | . . . . . . 7 |
13 | eeanv 2182 | . . . . . . 7 | |
14 | 12, 13 | sylibr 224 | . . . . . 6 |
15 | 9, 14 | anim12i 590 | . . . . 5 |
16 | ee4anv 2184 | . . . . 5 | |
17 | 15, 16 | sylibr 224 | . . . 4 |
18 | cgsex4g.1 | . . . . . 6 | |
19 | 18 | 2eximi 1763 | . . . . 5 |
20 | 19 | 2eximi 1763 | . . . 4 |
21 | 17, 20 | syl 17 | . . 3 |
22 | 1 | biimprcd 240 | . . . . . 6 |
23 | 22 | ancld 576 | . . . . 5 |
24 | 23 | 2eximdv 1848 | . . . 4 |
25 | 24 | 2eximdv 1848 | . . 3 |
26 | 21, 25 | syl5com 31 | . 2 |
27 | 4, 26 | impbid2 216 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 |
This theorem is referenced by: copsex4g 4959 brecop 7840 |
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