Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sbcel2gOLD Structured version   Unicode version

Theorem sbcel2gOLD 36761
 Description: Move proper substitution in and out of a membership relation. (Contributed by NM, 14-Nov-2005.) Obsolete as of 18-Aug-2018. Use sbcel2 3806 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbcel2gOLD
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbcel2gOLD
StepHypRef Expression
1 sbcel12gOLD 36760 . 2
2 csbconstg 3408 . . 3
32eleq1d 2491 . 2
41, 3bitrd 256 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wcel 1868  wsbc 3299  csb 3395 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-v 3083  df-sbc 3300  df-csb 3396 This theorem is referenced by:  sbcssOLD  36762  csbabgOLD  37069  csbunigOLD  37070  csbxpgOLD  37072  csbrngOLD  37075  sbcssgVD  37138  csbingVD  37139  csbunigVD  37153
 Copyright terms: Public domain W3C validator