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Theorem cgsexg 2979
 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 471 . . 3
32exlimiv 1644 . 2
4 elisset 2958 . . . 4
5 cgsexg.1 . . . . 5
65eximi 1585 . . . 4
74, 6syl 16 . . 3
81biimprcd 217 . . . . 5
98ancld 537 . . . 4
109eximdv 1632 . . 3
117, 10syl5com 28 . 2
123, 11impbid2 196 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
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