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Theorem cgsex2g 3143
Description: Implicit substitution inference for general classes. (Contributed by NM, 26-Jul-1995.)
Hypotheses
Ref Expression
cgsex2g.1
cgsex2g.2
Assertion
Ref Expression
cgsex2g
Distinct variable groups:   , ,   , ,   , ,

Proof of Theorem cgsex2g
StepHypRef Expression
1 cgsex2g.2 . . . 4
21biimpa 484 . . 3
32exlimivv 1723 . 2
4 elisset 3120 . . . . . 6
5 elisset 3120 . . . . . 6
64, 5anim12i 566 . . . . 5
7 eeanv 1988 . . . . 5
86, 7sylibr 212 . . . 4
9 cgsex2g.1 . . . . 5
1092eximi 1657 . . . 4
118, 10syl 16 . . 3
121biimprcd 225 . . . . 5
1312ancld 553 . . . 4
14132eximdv 1712 . . 3
1511, 14syl5com 30 . 2
163, 15impbid2 204 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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