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Theorem cgsex2g 2988
 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 471 . . 3
32exlimivv 1645 . 2
4 elisset 2966 . . . . . 6
5 elisset 2966 . . . . . 6
64, 5anim12i 550 . . . . 5
7 eeanv 1937 . . . . 5
86, 7sylibr 204 . . . 4
9 cgsex2g.1 . . . . 5
1092eximi 1586 . . . 4
118, 10syl 16 . . 3
121biimprcd 217 . . . . 5
1312ancld 537 . . . 4
14132eximdv 1634 . . 3
1511, 14syl5com 28 . 2
163, 15impbid2 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-6 1744  ax-7 1749  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958
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