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Theorem breq1i 3904
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 3900 . 2  |-  ( A  =  B  ->  ( A R C  <->  B R C ) )
31, 2ax-mp 5 1  |-  ( A R C  <->  B R C )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1314   class class class wbr 3897
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898
This theorem is referenced by:  eqbrtri  3917  brtpos0  6115  euen1  6662  euen1b  6663  2dom  6665  infglbti  6878  pr2nelem  7013  caucvgprprlemnbj  7465  caucvgprprlemmu  7467  caucvgprprlemaddq  7480  caucvgprprlem1  7481  gt0srpr  7520  caucvgsr  7574  mappsrprg  7576  map2psrprg  7577  pitonnlem1  7617  pitoregt0  7621  axprecex  7652  axpre-mulgt0  7659  axcaucvglemres  7671  lt0neg1  8194  le0neg1  8196  reclt1  8611  addltmul  8907  eluz2b1  9344  nn01to3  9358  xlt0neg1  9561  xle0neg1  9563  iccshftr  9717  iccshftl  9719  iccdil  9721  icccntr  9723  bernneq  10352  cbvsum  11069  expcnv  11213  oddge22np1  11474  nn0o1gt2  11498  isprm3  11695  dvdsnprmd  11702  pw2dvdslemn  11738  txmetcnp  12582
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