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Theorem breqtrri 3817
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
breqtrr.1  |-  A R B
breqtrr.2  |-  C  =  B
Assertion
Ref Expression
breqtrri  |-  A R C

Proof of Theorem breqtrri
StepHypRef Expression
1 breqtrr.1 . 2  |-  A R B
2 breqtrr.2 . . 3  |-  C  =  B
32eqcomi 2060 . 2  |-  B  =  C
41, 3breqtri 3815 1  |-  A R C
Colors of variables: wff set class
Syntax hints:    = wceq 1259   class class class wbr 3792
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793
This theorem is referenced by:  3brtr4i  3820  ensn1  6307  0lt1sr  6908  0le2  8080  2pos  8081  3pos  8084  4pos  8087  5pos  8090  6pos  8091  7pos  8092  8pos  8093  9pos  8094  1lt2  8152  2lt3  8153  3lt4  8155  4lt5  8158  5lt6  8162  6lt7  8167  7lt8  8173  8lt9  8180  nn0le2xi  8289  numltc  8452  declti  8464  sqge0i  9506  faclbnd2  9610  3dvdsdec  10176  n2dvdsm1  10225  n2dvds3  10227  ex-fl  10279
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