Theorem eqbrtrri 5125

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 5123	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1540   class class class wbr 5102

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 3403  df-v 3446  df-dif 3914  df-un 3916  df-ss 3928  df-nul 4293  df-if 4485  df-sn 4586  df-pr 4588  df-op 4592  df-br 5103

This theorem is referenced by:  3brtr3i  5131  expnass  14149  faclbnd4lem1  14234  sqrt2gt1lt2  15216  cos1bnd  16131  cos2bnd  16132  prdsvalstr  17391  ovolre  25402  pigt3  26403  pige3ALT  26405  atan1  26814  log2ublem1  26832  sqrtlim  26859  bposlem8  27178  chebbnd1  27359  norm-ii-i  31039  nmopadji  31992  unierri  32006  chnub  32911  ballotlem2  34453  hgt750lemd  34612  hgt750lem  34615  stoweidlem26  45997  wallispilem5  46040