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Theorem 3brtr3i 3964
 Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.)
Hypotheses
Ref Expression
3brtr3.1
3brtr3.2
3brtr3.3
Assertion
Ref Expression
3brtr3i

Proof of Theorem 3brtr3i
StepHypRef Expression
1 3brtr3.2 . . 3
2 3brtr3.1 . . 3
31, 2eqbrtrri 3958 . 2
4 3brtr3.3 . 2
53, 4breqtri 3960 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   class class class wbr 3936 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3079  df-sn 3537  df-pr 3538  df-op 3540  df-br 3937 This theorem is referenced by:  suplocsrlempr  7638  iap0  8966  ef01bndlem  11497
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