Theorem eqbrtrri 5123

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 2746	. 2 ⊢ 𝐵 = 𝐴
3		eqbrtrr.2	. 2 ⊢ 𝐴𝑅𝐶
4	2, 3	eqbrtri 5121	1 ⊢ 𝐵𝑅𝐶

Syntax hints:   = wceq 1542   class class class wbr 5100

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-br 5101

This theorem is referenced by:  3brtr3i  5129  expnass  14143  faclbnd4lem1  14228  sqrt2gt1lt2  15209  cos1bnd  16124  cos2bnd  16125  prdsvalstr  17384  chnub  18557  ovolre  25494  pigt3  26495  pige3ALT  26497  atan1  26906  log2ublem1  26924  sqrtlim  26951  bposlem8  27270  chebbnd1  27451  norm-ii-i  31225  nmopadji  32178  unierri  32192  ballotlem2  34667  hgt750lemd  34826  hgt750lem  34829  stoweidlem26  46384  wallispilem5  46427