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Theorem cgsex2g 2820
 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:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem cgsex2g
StepHypRef Expression
1 cgsex2g.2 . . . 4
21biimpa 470 . . 3
32exlimivv 1667 . 2
4 elisset 2798 . . . . . 6
5 elisset 2798 . . . . . 6
64, 5anim12i 549 . . . . 5
7 eeanv 1854 . . . . 5
86, 7sylibr 203 . . . 4
9 cgsex2g.1 . . . . 5
1092eximi 1564 . . . 4
118, 10syl 15 . . 3
121biimprcd 216 . . . . 5
1312ancld 536 . . . 4
14132eximdv 1610 . . 3
1511, 14syl5com 26 . 2
163, 15impbid2 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wex 1528   wceq 1623   wcel 1684 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-v 2790
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