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 2740	. 2 ⊢ 𝐵 = 𝐴
3		eqbrtrr.2	. 2 ⊢ 𝐴𝑅𝐶
4	2, 3	eqbrtri 5107	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1541   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 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

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 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-v 3438  df-dif 3900  df-un 3902  df-ss 3914  df-nul 4279  df-if 4471  df-sn 4572  df-pr 4574  df-op 4578  df-br 5087

This theorem is referenced by:  3brtr3i  5115  expnass  14110  faclbnd4lem1  14195  sqrt2gt1lt2  15176  cos1bnd  16091  cos2bnd  16092  prdsvalstr  17351  chnub  18523  ovolre  25448  pigt3  26449  pige3ALT  26451  atan1  26860  log2ublem1  26878  sqrtlim  26905  bposlem8  27224  chebbnd1  27405  norm-ii-i  31109  nmopadji  32062  unierri  32076  ballotlem2  34494  hgt750lemd  34653  hgt750lem  34656  stoweidlem26  46064  wallispilem5  46107