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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 𝐴𝑅𝐵
3brtr4.2 𝐶 = 𝐴
3brtr4.3 𝐷 = 𝐵
Assertion
Ref Expression
3brtr4i 𝐶𝑅𝐷

Proof of Theorem 3brtr4i
StepHypRef Expression
1 3brtr4.2 . . 3 𝐶 = 𝐴
2 3brtr4.1 . . 3 𝐴𝑅𝐵
31, 2eqbrtri 3949 . 2 𝐶𝑅𝐵
4 3brtr4.3 . 2 𝐷 = 𝐵
53, 4breqtrri 3955 1 𝐶𝑅𝐷
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  7226  0lt1sr  7585  ax0lt1  7696  declt  9221  decltc  9222  decle  9227  frecfzennn  10211  fsumabs  11246  2strbasg  12074  2stropg  12075
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