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Theorem breq12i 3938
 Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.) (Proof shortened by Eric Schmidt, 4-Apr-2007.)
Hypotheses
Ref Expression
breq1i.1
breq12i.2
Assertion
Ref Expression
breq12i

Proof of Theorem breq12i
StepHypRef Expression
1 breq1i.1 . 2
2 breq12i.2 . 2
3 breq12 3934 . 2
41, 2, 3mp2an 422 1
 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:  3brtr3g  3961  3brtr4g  3962  caovord2  5943  ltneg  8224  leneg  8227  inelr  8346  lt2sqi  10380  le2sqi  10381
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