Theorem eqbrtrri 5109

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 1-Aug-1999.)

Hypotheses

Ref	Expression
eqbrtrr.1	⊢ 𝐴 = 𝐵
eqbrtrr.2	⊢ 𝐴𝑅𝐶

Assertion

Ref	Expression
eqbrtrri	⊢ 𝐵𝑅𝐶

Proof of Theorem eqbrtrri

Step	Hyp	Ref	Expression
1		eqbrtrr.1	. . 3 ⊢ 𝐴 = 𝐵
2	1	eqcomi 2746	. 2 ⊢ 𝐵 = 𝐴
3		eqbrtrr.2	. 2 ⊢ 𝐴𝑅𝐶
4	2, 3	eqbrtri 5107	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1542   class class class wbr 5086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-br 5087

This theorem is referenced by:  3brtr3i  5115  expnass  14161  faclbnd4lem1  14246  sqrt2gt1lt2  15227  cos1bnd  16145  cos2bnd  16146  prdsvalstr  17406  chnub  18579  ovolre  25502  pigt3  26495  pige3ALT  26497  atan1  26905  log2ublem1  26923  sqrtlim  26950  bposlem8  27268  chebbnd1  27449  norm-ii-i  31223  nmopadji  32176  unierri  32190  ballotlem2  34649  hgt750lemd  34808  hgt750lem  34811  stoweidlem26  46472  wallispilem5  46515