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Theorem breqan12d 3779
 Description: Equality deduction for a binary relation. (Contributed by NM, 8-Feb-1996.)
Hypotheses
Ref Expression
breq1d.1
breqan12i.2
Assertion
Ref Expression
breqan12d

Proof of Theorem breqan12d
StepHypRef Expression
1 breq1d.1 . 2
2 breqan12i.2 . 2
3 breq12 3769 . 2
41, 2, 3syl2an 273 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243   class class class wbr 3764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765 This theorem is referenced by:  breqan12rd  3780  sosng  4413  isoresbr  5449  isoid  5450  isores3  5455  isoini2  5458  ofrfval  5720  oviec  6212  enqbreq2  6455  ltresr2  6916  axpre-ltadd  6960  leltadd  7442  xltneg  8749  lt2sq  9327  le2sq  9328  sqrtle  9634  sqrtlt  9635  absext  9661
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