Theorem breq12i 4461

Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.) (Proof shortened by Eric Schmidt, 4-Apr-2007.)

Hypotheses

Ref	Expression
breq1i.1
breq12i.2

Assertion

Ref	Expression
breq12i

Proof of Theorem breq12i

Step	Hyp	Ref	Expression
1		breq1i.1	. 2
2		breq12i.2	. 2
3		breq12 4457	. 2
4	1, 2, 3	mp2an 672	1

Syntax hints:  <->wb 184  =wceq 1395   class class class wbr 4452

This theorem is referenced by:  3brtr3g  4483  3brtr4g  4484  caovord2  6487  domunfican  7813  ltsonq  9368  ltanq  9370  ltmnq  9371  prlem934  9432  prlem936  9446  ltsosr  9492  ltasr  9498  ltneg  10077  leneg  10080  inelr  10551  lt2sqi  12256  le2sqi  12257  nn0le2msqi  12347  axlowdimlem6  24250  mdsldmd1i  27250  divcnvlin  29118  iscmgmALT  32548  iscsgrpALT  32550

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