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Theorem sbcel1gvOLD 3393
Description: Class substitution into a membership relation. (Contributed by NM, 17-Nov-2006.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) Obsolete as of 17-Aug-2018. Use sbcel1v 3392 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbcel1gvOLD
Distinct variable group:   ,

Proof of Theorem sbcel1gvOLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3330 . 2
2 eleq1 2529 . 2
3 clelsb3 2578 . 2
41, 2, 3vtoclbg 3168 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  [wsb 1739  e.wcel 1818  [.wsbc 3327
This theorem is referenced by:  sbcoreleleqVD  33659  onfrALTlem4VD  33686
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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