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Theorem sbcel2g 2871
 Description: Move proper substitution in and out of a membership relation. (Contributed by NM, 14-Nov-2005.)
Assertion
Ref Expression
sbcel2g
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbcel2g
StepHypRef Expression
1 sbcel12g 2865 . 2
2 csbconstg 2864 . . 3
32eleq1d 2106 . 2
41, 3bitrd 177 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wcel 1393  wsbc 2764  csb 2852 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-sbc 2765  df-csb 2853 This theorem is referenced by:  csbcomg  2873  sbccsbg  2878  sbnfc2  2906  csbabg  2907  sbcssg  3330  csbunig  3588  csbxpg  4421  csbdmg  4529  csbrng  4782  bj-sels  10034
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