Theorem eqbrtrri 5130

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 2738	. 2 ⊢ 𝐵 = 𝐴
3		eqbrtrr.2	. 2 ⊢ 𝐴𝑅𝐶
4	2, 3	eqbrtri 5128	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1540   class class class wbr 5107

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-rab 3406  df-v 3449  df-dif 3917  df-un 3919  df-ss 3931  df-nul 4297  df-if 4489  df-sn 4590  df-pr 4592  df-op 4596  df-br 5108

This theorem is referenced by:  3brtr3i  5136  expnass  14173  faclbnd4lem1  14258  sqrt2gt1lt2  15240  cos1bnd  16155  cos2bnd  16156  prdsvalstr  17415  ovolre  25426  pigt3  26427  pige3ALT  26429  atan1  26838  log2ublem1  26856  sqrtlim  26883  bposlem8  27202  chebbnd1  27383  norm-ii-i  31066  nmopadji  32019  unierri  32033  chnub  32938  ballotlem2  34480  hgt750lemd  34639  hgt750lem  34642  stoweidlem26  46024  wallispilem5  46067