Theorem breqtrri 3920

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

Step	Hyp	Ref	Expression
1		breqtrr.1	. 2 |- A R B
2		breqtrr.2	. . 3 |- C = B
3	2	eqcomi 2119	. 2 |- B = C
4	1, 3	breqtri 3918	1 |- A R C

Syntax hints:   = wceq 1314   class class class wbr 3895

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 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 2244  df-v 2659  df-un 3041  df-sn 3499  df-pr 3500  df-op 3502  df-br 3896

This theorem is referenced by:  3brtr4i  3923  ensn1  6644  0lt1sr  7508  0le2  8720  2pos  8721  3pos  8724  4pos  8727  5pos  8730  6pos  8731  7pos  8732  8pos  8733  9pos  8734  1lt2  8793  2lt3  8794  3lt4  8796  4lt5  8799  5lt6  8803  6lt7  8808  7lt8  8814  8lt9  8821  nn0le2xi  8931  numltc  9111  declti  9123  sqge0i  10272  faclbnd2  10381  ege2le3  11228  cos2bnd  11318  3dvdsdec  11410  n2dvdsm1  11458  n2dvds3  11460  ex-fl  12630  pw1dom2  12882