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Theorem breqtrri 3923
 Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
breqtrr.1 𝐴𝑅𝐵
breqtrr.2 𝐶 = 𝐵
Assertion
Ref Expression
breqtrri 𝐴𝑅𝐶

Proof of Theorem breqtrri
StepHypRef Expression
1 breqtrr.1 . 2 𝐴𝑅𝐵
2 breqtrr.2 . . 3 𝐶 = 𝐵
32eqcomi 2119 . 2 𝐵 = 𝐶
41, 3breqtri 3921 1 𝐴𝑅𝐶
 Colors of variables: wff set class Syntax hints:   = wceq 1314   class class class wbr 3897 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898 This theorem is referenced by:  3brtr4i  3926  ensn1  6656  0lt1sr  7537  0le2  8770  2pos  8771  3pos  8774  4pos  8777  5pos  8780  6pos  8781  7pos  8782  8pos  8783  9pos  8784  1lt2  8843  2lt3  8844  3lt4  8846  4lt5  8849  5lt6  8853  6lt7  8858  7lt8  8864  8lt9  8871  nn0le2xi  8981  numltc  9161  declti  9173  sqge0i  10330  faclbnd2  10439  ege2le3  11287  cos2bnd  11377  3dvdsdec  11469  n2dvdsm1  11517  n2dvds3  11519  dveflem  12761  ex-fl  12771  pw1dom2  13024
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