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Theorem breq1i 3800
Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.)
Hypothesis
Ref Expression
breq1i.1  |-  A  =  B
Assertion
Ref Expression
breq1i  |-  ( A R C  <->  B R C )

Proof of Theorem breq1i
StepHypRef Expression
1 breq1i.1 . 2  |-  A  =  B
2 breq1 3796 . 2  |-  ( A  =  B  ->  ( A R C  <->  B R C ) )
31, 2ax-mp 7 1  |-  ( A R C  <->  B R C )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1285   class class class wbr 3793
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794
This theorem is referenced by:  eqbrtri  3812  brtpos0  5901  euen1  6349  euen1b  6350  2dom  6352  infglbti  6497  pr2nelem  6519  caucvgprprlemnbj  6945  caucvgprprlemmu  6947  caucvgprprlemaddq  6960  caucvgprprlem1  6961  gt0srpr  6987  caucvgsr  7040  pitonnlem1  7075  pitoregt0  7079  axprecex  7108  axpre-mulgt0  7115  axcaucvglemres  7127  lt0neg1  7639  le0neg1  7641  reclt1  8041  addltmul  8334  eluz2b1  8769  nn01to3  8783  xlt0neg1  8981  xle0neg1  8983  iccshftr  9092  iccshftl  9094  iccdil  9096  icccntr  9098  bernneq  9690  oddge22np1  10425  nn0o1gt2  10449  isprm3  10644  dvdsnprmd  10651  pw2dvdslemn  10687
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