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Theorem sbcel2gOLD 3832
 Description: Move proper substitution in and out of a membership relation. (Contributed by NM, 14-Nov-2005.) Obsolete as of 18-Aug-2018. Use sbcel2 3831 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbcel2gOLD
Distinct variable group:   ,

Proof of Theorem sbcel2gOLD
StepHypRef Expression
1 sbcel12gOLD 3824 . 2
2 csbconstg 3447 . . 3
32eleq1d 2526 . 2
41, 3bitrd 253 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:  csbcomgOLD  3838  sbccsbgOLD  3850  csbabgOLD  3856  csbunigOLD  4278  csbxpgOLD  5087  csbrngOLD  5474  sbcssOLD  33313  sbcssgVD  33683  csbingVD  33684  csbunigVD  33698 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-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
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