Theorem eqbrtrr 2078

Description: Substitution of equal classes into a binary relation.

Hypotheses

Ref	Expression
eqbrtrr.1	⊢ A = B
eqbrtrr.2	⊢ ARC

Assertion

Ref	Expression
eqbrtrr	⊢ BRC

Proof of Theorem eqbrtrr

Step	Hyp	Ref	Expression
1		eqbrtrr.1	. . 3 ⊢ A = B
2	1	cleqcomi 1105	. 2 ⊢ B = A
3		eqbrtrr.2	. 2 ⊢ ARC
4	2, 3	eqbrtr 2076	1 ⊢ BRC

Syntax hints:   = wceq 1091   class class class wbr 2054

This theorem is referenced by:  3brtr3 2084  nn0addge1 4560  nnlesq 4718  nnesq 4720  nn0opthlem2 4723  sqrlem1 4731  sqrlem11 4741  sqrlem15 4745  sqr2irrlem1 4777  releabs 4858  infdif 4948  norm-ii 5086  projlem13 5205  projlem15 5207

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-sn 1811  df-pr 1812  df-op 1815  df-br 2063

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