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Theorem cgsex4g 2892
 Description: An implicit substitution inference for 4 general classes. (Contributed by NM, 5-Aug-1995.)
Hypotheses
Ref Expression
cgsex4g.1
cgsex4g.2
Assertion
Ref Expression
cgsex4g
Distinct variable groups:   ,,,,   ,,,,   ,,,,   ,,,,   ,,,,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,,)

Proof of Theorem cgsex4g
StepHypRef Expression
1 cgsex4g.2 . . . . 5
21biimpa 470 . . . 4
32exlimivv 1635 . . 3
43exlimivv 1635 . 2
5 elisset 2869 . . . . . . . 8
6 elisset 2869 . . . . . . . 8
75, 6anim12i 549 . . . . . . 7
8 eeanv 1913 . . . . . . 7
97, 8sylibr 203 . . . . . 6
10 elisset 2869 . . . . . . . 8
11 elisset 2869 . . . . . . . 8
1210, 11anim12i 549 . . . . . . 7
13 eeanv 1913 . . . . . . 7
1412, 13sylibr 203 . . . . . 6
159, 14anim12i 549 . . . . 5
16 ee4anv 1915 . . . . 5
1715, 16sylibr 203 . . . 4
18 cgsex4g.1 . . . . . 6
19182eximi 1577 . . . . 5
20192eximi 1577 . . . 4
2117, 20syl 15 . . 3
221biimprcd 216 . . . . . 6
2322ancld 536 . . . . 5
24232eximdv 1624 . . . 4
25242eximdv 1624 . . 3
2621, 25syl5com 26 . 2
274, 26impbid2 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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