Theorem breq12i 2070

Description: Equality inference for binary relation.

Hypotheses

Ref	Expression
breq1i.1	|- A = B
breq12i.2	|- C = D

Assertion

Ref	Expression
breq12i	|- (ARC <-> BRD)

Proof of Theorem breq12i

Step	Hyp	Ref	Expression
1		breq1i.1	. . 3 |- A = B
2	1	breq1i 2068	. 2 |- (ARC <-> BRC)
3		breq12i.2	. . 3 |- C = D
4	3	breq2i 2069	. 2 |- (BRC <-> BRD)
5	2, 4	bitr 151	1 |- (ARC <-> BRD)

Syntax hints:   <-> wb 127   = wceq 1091   class class class wbr 2054

This theorem is referenced by:  3brtr3g 2087  3brtr4g 2088  caoprord2 3071  ltsopq 3869  ltapq 3870  ltmpq 3871  ltaddpq 3873  prlem936a 3947  ltsosr 3997  ltasr 4003  ltpsrpr 4013  ltadd1 4313  leadd2 4315  ltneg 4330  lesub0 4341  subge0 4342  ltmul2 4395  lemul1 4397  ltdivi 4398  ltreci 4409  halfpos 4421  inelr 4527  lt2sqe 4700  le2sqe 4701  discrlem1 4713  nn0le2sqet 4721  sqrlem16 4746  ruclem2 4886  ruclem15 4899  pjthlem1 5225  mdsym 5784

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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