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Theorem 3brtr4i 3958
 Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.)
Hypotheses
Ref Expression
3brtr4.1
3brtr4.2
3brtr4.3
Assertion
Ref Expression
3brtr4i

Proof of Theorem 3brtr4i
StepHypRef Expression
1 3brtr4.2 . . 3
2 3brtr4.1 . . 3
31, 2eqbrtri 3949 . 2
4 3brtr4.3 . 2
53, 4breqtrri 3955 1
 Colors of variables: wff set class Syntax hints:   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:  1lt2nq  7221  0lt1sr  7580  ax0lt1  7691  declt  9216  decltc  9217  decle  9222  frecfzennn  10206  fsumabs  11241  2strbasg  12070  2stropg  12071
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