Theorem eqbrtrri 5118

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 5116	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1540   class class class wbr 5095

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 3397  df-v 3440  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4479  df-sn 4580  df-pr 4582  df-op 4586  df-br 5096

This theorem is referenced by:  3brtr3i  5124  expnass  14134  faclbnd4lem1  14219  sqrt2gt1lt2  15200  cos1bnd  16115  cos2bnd  16116  prdsvalstr  17375  ovolre  25443  pigt3  26444  pige3ALT  26446  atan1  26855  log2ublem1  26873  sqrtlim  26900  bposlem8  27219  chebbnd1  27400  norm-ii-i  31100  nmopadji  32053  unierri  32067  chnub  32973  ballotlem2  34476  hgt750lemd  34635  hgt750lem  34638  stoweidlem26  46027  wallispilem5  46070