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Theorem cgsexg 2657
 Description: Implicit substitution inference for general classes. (Contributed by NM, 26-Aug-2007.)
Hypotheses
Ref Expression
cgsexg.1
cgsexg.2
Assertion
Ref Expression
cgsexg
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem cgsexg
StepHypRef Expression
1 cgsexg.2 . . . 4
21biimpa 291 . . 3
32exlimiv 1535 . 2
4 elisset 2636 . . . 4
5 cgsexg.1 . . . . 5
65eximi 1537 . . . 4
74, 6syl 14 . . 3
81biimprcd 159 . . . . 5
98ancld 319 . . . 4
109eximdv 1809 . . 3
117, 10syl5com 29 . 2
123, 11impbid2 142 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1290  wex 1427   wcel 1439 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-v 2624 This theorem is referenced by: (None)
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