Theorem eqbrtrri 5116

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 5114	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1541   class class class wbr 5093

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 4283  df-if 4475  df-sn 4576  df-pr 4578  df-op 4582  df-br 5094

This theorem is referenced by:  3brtr3i  5122  expnass  14121  faclbnd4lem1  14206  sqrt2gt1lt2  15187  cos1bnd  16102  cos2bnd  16103  prdsvalstr  17362  chnub  18534  ovolre  25459  pigt3  26460  pige3ALT  26462  atan1  26871  log2ublem1  26889  sqrtlim  26916  bposlem8  27235  chebbnd1  27416  norm-ii-i  31124  nmopadji  32077  unierri  32091  ballotlem2  34509  hgt750lemd  34668  hgt750lem  34671  stoweidlem26  46129  wallispilem5  46172