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Theorem sbcel2gv 3213
 Description: Class substitution into a membership relation. (Contributed by NM, 17-Nov-2006.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
sbcel2gv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbcel2gv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2496 . 2
2 eleq2 2496 . 2
31, 2sbcie2g 3186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wcel 1725  wsbc 3153 This theorem is referenced by:  csbvarg  3270  sbcoreleleq  28546  trsbc  28552  onfrALTlem5  28555  sbcoreleleqVD  28898  trsbcVD  28916  onfrALTlem5VD  28924  bnj92  29160  bnj539  29189 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
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