Theorem eqbrtrri 5108

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 2745	. 2 ⊢ 𝐵 = 𝐴
3		eqbrtrr.2	. 2 ⊢ 𝐴𝑅𝐶
4	2, 3	eqbrtri 5106	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1542   class class class wbr 5085

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 2708

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 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-dif 3892  df-un 3894  df-ss 3906  df-nul 4274  df-if 4467  df-sn 4568  df-pr 4570  df-op 4574  df-br 5086

This theorem is referenced by:  3brtr3i  5114  expnass  14170  faclbnd4lem1  14255  sqrt2gt1lt2  15236  cos1bnd  16154  cos2bnd  16155  prdsvalstr  17415  chnub  18588  ovolre  25492  pigt3  26482  pige3ALT  26484  atan1  26892  log2ublem1  26910  sqrtlim  26936  bposlem8  27254  chebbnd1  27435  norm-ii-i  31208  nmopadji  32161  unierri  32175  ballotlem2  34633  hgt750lemd  34792  hgt750lem  34795  stoweidlem26  46454  wallispilem5  46497