Theorem eqbrtrrd 2637

Description: Substitution of equal classes into a binary relation.

Hypotheses

Ref	Expression
eqbrtrrd.1	|- (ph -> A = B)
eqbrtrrd.2	|- (ph -> ARC)

Assertion

Ref	Expression
eqbrtrrd	|- (ph -> BRC)

Proof of Theorem eqbrtrrd

Step	Hyp	Ref	Expression
1		eqbrtrrd.1	. . 3 |- (ph -> A = B)
2	1	eqcomd 1480	. 2 |- (ph -> B = A)
3		eqbrtrrd.2	. 2 |- (ph -> ARC)
4	2, 3	eqbrtrd 2635	1 |- (ph -> BRC)

Syntax hints:   -> wi 3   = wceq 956   class class class wbr 2619

This theorem is referenced by:  fodomfiOLD 4566  lemulge11t 5848  flhalft 6246  ser1mono 6337  abs3dift 6899  abs2dift 6902  caubnd 6926  facwordit 6944  faclbnd4lem1 6948  facavgt 6955  fsumcmp0 7041  fsumabs 7043  serzcmp0 7055  2climnn 7102  2climnn0 7103  climmullem3 7122  climre 7151  climim 7152  climcau 7156  caucvg 7163  ser1cmp0 7175  isumclim5t 7202  recncf 7276  imcncf 7277  efcnlem1 7419  sin01bndlem3 7469  cos01bndlem3 7471  unctb 7577  bcthlem26 8024  nvabs 8301  normpyct 9013  nmophm 9961  lnopcon 9963  lnfncon 9990  hmopidmchlem 10078  hstlet 10157  hstlest 10158  stle 10167  mslb1 10629

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050  df-sn 2412  df-pr 2413  df-op 2416  df-br 2620

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