Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbcbr2g Unicode version

Theorem sbcbr2g 4508
 Description: Move substitution in and out of a binary relation. (Contributed by NM, 13-Dec-2005.)
Assertion
Ref Expression
sbcbr2g
Distinct variable groups:   ,   ,

Proof of Theorem sbcbr2g
StepHypRef Expression
1 sbcbr12g 4506 . 2
2 csbconstg 3447 . . 3
32breq1d 4462 . 2
41, 3bitrd 253 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  e.wcel 1818  [.wsbc 3327  [_csb 3434   class class class wbr 4452 This theorem is referenced by:  telgsums  17022  fvmptnn04if  19350  bnj110  33916  frege72  37963 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453
 Copyright terms: Public domain W3C validator