Theorem breqan12rd 4468

Description: Equality deduction for a binary relation. (Contributed by NM, 8-Feb-1996.)

Hypotheses

Ref	Expression
breq1d.1
breqan12i.2

Assertion

Ref	Expression
breqan12rd

Proof of Theorem breqan12rd

Step	Hyp	Ref	Expression
1		breq1d.1	. . 3
2		breqan12i.2	. . 3
3	1, 2	breqan12d 4467	. 2
4	3	ancoms 453	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395   class class class wbr 4452

This theorem is referenced by:  f1oweALT  6784  ledivdiv  10459  xltnegi  11444  ramub1lem1  14544  dvferm1  22386  dvferm2  22388  dvivthlem1  22409  ulmdvlem3  22797  lgsquad  23632  areacirclem4  30110  areacirclem5  30111

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453