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Theorem 3brtr4g 4484
 Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 16-Jan-1997.)
Hypotheses
Ref Expression
3brtr4g.1
3brtr4g.2
3brtr4g.3
Assertion
Ref Expression
3brtr4g

Proof of Theorem 3brtr4g
StepHypRef Expression
1 3brtr4g.1 . 2
2 3brtr4g.2 . . 3
3 3brtr4g.3 . . 3
42, 3breq12i 4461 . 2
51, 4sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395   class class class wbr 4452 This theorem is referenced by:  syl5eqbr  4485  limensuci  7713  infensuc  7715  rlimneg  13469  isumsup2  13658  crt  14308  4sqlem6  14461  gzrngunit  18483  matgsum  18939  ovolunlem1a  21907  ovolfiniun  21912  ioombl1lem1  21968  ioombl1lem4  21971  iblss  22211  itgle  22216  dvfsumlem3  22429  emcllem6  23330  pntpbnd1a  23770  ostth2lem4  23821  omsmon  28267  itg2gt0cn  30070  fourierdlem103  31992  fourierdlem104  31993  dalem-cly  35395  dalem10  35397 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-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-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
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