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Theorem sbcel1v 3392
Description: Class substitution into a membership relation. (Contributed by NM, 17-Aug-2018.)
Assertion
Ref Expression
sbcel1v
Distinct variable group:   ,

Proof of Theorem sbcel1v
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3337 . 2
2 elex 3118 . 2
3 dfsbcq2 3330 . . 3
4 eleq1 2529 . . 3
5 clelsb3 2578 . . 3
63, 4, 5vtoclbg 3168 . 2
71, 2, 6pm5.21nii 353 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  [wsb 1739  e.wcel 1818   cvv 3109  [.wsbc 3327
This theorem is referenced by:  tfinds2  6698  filuni  20386  f1od2  27547  sbcoreleleq  33306  onfrALTlem4  33315  bnj110  33916
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-v 3111  df-sbc 3328
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