New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  sbcel2g Unicode version

Theorem sbcel2g 3157
 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 3151 . 2
2 csbconstg 3150 . . 3
32eleq1d 2419 . 2
41, 3bitrd 244 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wcel 1710  wsbc 3046  csb 3136 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137 This theorem is referenced by:  csbcomg  3159  sbccsbg  3164  sbnfc2  3196  csbabg  3197  sbcss  3660  csbunig  3899  csbxpg  4813  csbrng  4966
 Copyright terms: Public domain W3C validator