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Theorem breq12i 4213
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 4209 . 2
41, 2, 3mp2an 654 1
Colors of variables: wff set class
Syntax hints:  <->wb 177  =wceq 1652   class class class wbr 4204
This theorem is referenced by:  3brtr3g  4235  3brtr4g  4236  caovord2  6251  domunfican  7371  ltsonq  8838  ltanq  8840  ltmnq  8841  prlem934  8902  prlem936  8916  ltsosr  8961  ltasr  8967  ltneg  9520  leneg  9523  inelr  9982  lt2sqi  11462  le2sqi  11463  nn0le2msqi  11552  mdsldmd1i  23826  divcnvlin  25204  axlowdimlem6  25878
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205
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