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Theorem breq12i 4252
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
StepHypRef Expression
1 breq1i.1 . 2
2 breq12i.2 . 2
3 breq12 4248 . 2
41, 2, 3mp2an 655 1
Colors of variables: wff set class
Syntax hints:  <->wb 178  =wceq 1654   class class class wbr 4243
This theorem is referenced by:  3brtr3g  4274  3brtr4g  4275  caovord2  6309  domunfican  7428  ltsonq  8897  ltanq  8899  ltmnq  8900  prlem934  8961  prlem936  8975  ltsosr  9020  ltasr  9026  ltneg  9579  leneg  9582  inelr  10041  lt2sqi  11521  le2sqi  11522  nn0le2msqi  11611  mdsldmd1i  23885  divcnvlin  25316  axlowdimlem6  25990
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3766  df-sn 3847  df-pr 3848  df-op 3850  df-br 4244
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