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Theorem sbcel1gv 3184
 Description: Class substitution into a membership relation. (Contributed by NM, 17-Nov-2006.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
sbcel1gv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbcel1gv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3128 . 2
2 eleq1 2468 . 2
3 clelsb3 2510 . 2
41, 2, 3vtoclbg 2976 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wsb 1655   wcel 1721  wsbc 3125 This theorem is referenced by:  tfinds2  4806  filuni  17874  sbcoreleleq  28334  onfrALTlem4  28344  sbcoreleleqVD  28684  onfrALTlem4VD  28711  bnj110  28939 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-v 2922  df-sbc 3126
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