Theorem eqbrtrri 5076

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 5074	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1543   class class class wbr 5053

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3070  df-v 3410  df-dif 3869  df-un 3871  df-nul 4238  df-if 4440  df-sn 4542  df-pr 4544  df-op 4548  df-br 5054

This theorem is referenced by:  3brtr3i  5082  expnass  13776  faclbnd4lem1  13859  sqrt2gt1lt2  14838  cos1bnd  15748  cos2bnd  15749  2strstr1  16781  prdsvalstr  16957  ovolre  24422  pigt3  25407  pige3ALT  25409  atan1  25811  log2ublem1  25829  sqrtlim  25855  bposlem8  26172  chebbnd1  26353  norm-ii-i  29218  nmopadji  30171  unierri  30185  ballotlem2  32167  hgt750lemd  32340  hgt750lem  32343  stoweidlem26  43242  wallispilem5  43285