Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbcbr12g Structured version   Unicode version

Theorem sbcbr12g 4265
 Description: Move substitution in and out of a binary relation. (Contributed by NM, 13-Dec-2005.)
Assertion
Ref Expression
sbcbr12g
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem sbcbr12g
StepHypRef Expression
1 sbcbrg 4264 . 2
2 csbconstg 3267 . . 3
32breqd 4226 . 2
41, 3bitrd 246 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wcel 1726  wsbc 3163  csb 3253   class class class wbr 4215 This theorem is referenced by:  sbcbr1g  4266  sbcbr2g  4267  cdlemk39s  31810 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216
 Copyright terms: Public domain W3C validator