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Theorem sbcel1g 3829
Description: Move proper substitution in and out of a membership relation. Note that the scope of [.A x]. is the wff , whereas the scope of [_A x]_ is the class . (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
sbcel1g
Distinct variable group:   ,

Proof of Theorem sbcel1g
StepHypRef Expression
1 sbcel12 3823 . 2
2 csbconstg 3447 . . 3
32eleq2d 2527 . 2
41, 3syl5bb 257 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  e.wcel 1818  [.wsbc 3327  [_csb 3434
This theorem is referenced by:  rspcsbela  3853  wunnat  15325  catcfuccl  15436  nbgraopALT  24424  rusgrasn  24945  esumpfinvalf  28082  measiuns  28188  finixpnum  30038  fprodcllemf  31591  ellimcabssub0  31623  bj-sbel1  34472  renegclALT  34694  cdlemk35s  36663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785
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