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Theorem breq2i 3937
 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 3933 . 2 (𝐴 = 𝐵 → (𝐶𝑅𝐴𝐶𝑅𝐵))
31, 2ax-mp 5 1 (𝐶𝑅𝐴𝐶𝑅𝐵)
 Colors of variables: wff set class Syntax hints:   ↔ wb 104   = wceq 1331   class class class wbr 3929 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930 This theorem is referenced by:  breqtri  3953  en1  6693  snnen2og  6753  1nen2  6755  pm54.43  7053  caucvgprprlemval  7510  caucvgprprlemmu  7517  caucvgsr  7624  pitonnlem1  7667  lt0neg2  8245  le0neg2  8247  negap0  8406  recexaplem2  8427  recgt1  8669  crap0  8730  addltmul  8970  nn0lt10b  9145  nn0lt2  9146  3halfnz  9162  xlt0neg2  9636  xle0neg2  9638  iccshftr  9791  iccshftl  9793  iccdil  9795  icccntr  9797  fihashen1  10559  cjap0  10693  abs00ap  10848  xrmaxiflemval  11033  mertenslem2  11319  mertensabs  11320  3dvdsdec  11575  3dvds2dec  11576  ndvdsi  11643  3prm  11822  prmfac1  11843  sinhalfpilem  12896  sincosq1lem  12930  sincosq1sgn  12931  sincosq2sgn  12932  sincosq3sgn  12933  sincosq4sgn  12934
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