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Theorem 3brtr4i 3821
 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 3812 . 2
4 3brtr4.3 . 2
53, 4breqtrri 3818 1
 Colors of variables: wff set class Syntax hints:   wceq 1285   class class class wbr 3793 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794 This theorem is referenced by:  1lt2nq  6658  0lt1sr  7004  ax0lt1  7104  declt  8585  decltc  8586  decle  8591  frecfzennn  9508
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