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Theorem breqtrri 4016
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 2174 . 2 𝐵 = 𝐶
41, 3breqtri 4014 1 𝐴𝑅𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1348   class class class wbr 3989
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-sn 3589  df-pr 3590  df-op 3592  df-br 3990
This theorem is referenced by:  3brtr4i  4019  ensn1  6774  pw1dom2  7204  0lt1sr  7727  0le2  8968  2pos  8969  3pos  8972  4pos  8975  5pos  8978  6pos  8979  7pos  8980  8pos  8981  9pos  8982  1lt2  9047  2lt3  9048  3lt4  9050  4lt5  9053  5lt6  9057  6lt7  9062  7lt8  9068  8lt9  9075  nn0le2xi  9185  numltc  9368  declti  9380  sqge0i  10562  faclbnd2  10676  ege2le3  11634  cos2bnd  11723  3dvdsdec  11824  n2dvdsm1  11872  n2dvds3  11874  pockthi  12310  dveflem  13481  tangtx  13553  lgsdir2lem2  13724  ex-fl  13760
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