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Theorem opeq1d 3546
Description: Equality deduction for ordered pairs. (Contributed by NM, 16-Dec-2006.)
Hypothesis
Ref Expression
opeq1d.1
Assertion
Ref Expression
opeq1d  <. ,  C >.  <. ,  C >.

Proof of Theorem opeq1d
StepHypRef Expression
1 opeq1d.1 . 2
2 opeq1 3540 . 2  <. ,  C >.  <. ,  C >.
31, 2syl 14 1  <. ,  C >.  <. ,  C >.
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   <.cop 3370
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376
This theorem is referenced by:  oteq1  3549  oteq2  3550  opth  3965  cbvoprab2  5519  dfplpq2  6338  ltexnqq  6391  nnanq0  6440  addpinq1  6446  prarloclemlo  6476  prarloclem3  6479  prarloclem5  6482  pitonnlem2  6703  pitonn  6704  ax1rid  6721  axrnegex  6723  fseq1m1p1  8687  frecuzrdglem  8838
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