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Theorem sbcbr2g 4264
 Description: Move substitution in and out of a binary relation. (Contributed by NM, 13-Dec-2005.)
Assertion
Ref Expression
sbcbr2g
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbcbr2g
StepHypRef Expression
1 sbcbr12g 4262 . 2
2 csbconstg 3265 . . 3
32breq1d 4222 . 2
41, 3bitrd 245 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wcel 1725  wsbc 3161  csb 3251   class class class wbr 4212 This theorem is referenced by:  bnj110  29229 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213
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