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Theorem breq2i 4026
Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.)
Hypothesis
Ref Expression
breq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
breq2i (𝐶𝑅𝐴𝐶𝑅𝐵)

Proof of Theorem breq2i
StepHypRef Expression
1 breq1i.1 . 2 𝐴 = 𝐵
2 breq2 4022 . 2 (𝐴 = 𝐵 → (𝐶𝑅𝐴𝐶𝑅𝐵))
31, 2ax-mp 5 1 (𝐶𝑅𝐴𝐶𝑅𝐵)
Colors of variables: wff set class
Syntax hints:  wb 105   = wceq 1364   class class class wbr 4018
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614  df-op 3616  df-br 4019
This theorem is referenced by:  breqtri  4043  en1  6824  snnen2og  6886  1nen2  6888  pm54.43  7218  caucvgprprlemval  7716  caucvgprprlemmu  7723  caucvgsr  7830  pitonnlem1  7873  lt0neg2  8455  le0neg2  8457  negap0  8616  recexaplem2  8638  recgt1  8883  crap0  8944  addltmul  9184  nn0lt10b  9362  nn0lt2  9363  3halfnz  9379  xlt0neg2  9868  xle0neg2  9870  iccshftr  10023  iccshftl  10025  iccdil  10027  icccntr  10029  fihashen1  10810  cjap0  10947  abs00ap  11102  xrmaxiflemval  11289  mertenslem2  11575  mertensabs  11576  3dvdsdec  11901  3dvds2dec  11902  ndvdsi  11969  3prm  12159  prmfac1  12183  prm23lt5  12294  sinhalfpilem  14664  sincosq1lem  14698  sincosq1sgn  14699  sincosq2sgn  14700  sincosq3sgn  14701  sincosq4sgn  14702  logrpap0b  14749  2lgsoddprmlem3  14912
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