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Theorem cgsex2g 2722
 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 294 . . 3
32exlimivv 1868 . 2
4 elisset 2700 . . . . . 6
5 elisset 2700 . . . . . 6
64, 5anim12i 336 . . . . 5
7 eeanv 1904 . . . . 5
86, 7sylibr 133 . . . 4
9 cgsex2g.1 . . . . 5
1092eximi 1580 . . . 4
118, 10syl 14 . . 3
121biimprcd 159 . . . . 5
1312ancld 323 . . . 4
14132eximdv 1854 . . 3
1511, 14syl5com 29 . 2
163, 15impbid2 142 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331  wex 1468   wcel 1480 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688 This theorem is referenced by: (None)
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