Theorem eqbrtrri 5121

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 5119	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1541   class class class wbr 5098

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3400  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-if 4480  df-sn 4581  df-pr 4583  df-op 4587  df-br 5099

This theorem is referenced by:  3brtr3i  5127  expnass  14131  faclbnd4lem1  14216  sqrt2gt1lt2  15197  cos1bnd  16112  cos2bnd  16113  prdsvalstr  17372  chnub  18545  ovolre  25482  pigt3  26483  pige3ALT  26485  atan1  26894  log2ublem1  26912  sqrtlim  26939  bposlem8  27258  chebbnd1  27439  norm-ii-i  31212  nmopadji  32165  unierri  32179  ballotlem2  34646  hgt750lemd  34805  hgt750lem  34808  stoweidlem26  46270  wallispilem5  46313