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Theorem opeq2d 3547
Description: Equality deduction for ordered pairs. (Contributed by NM, 16-Dec-2006.)
Hypothesis
Ref Expression
opeq1d.1
Assertion
Ref Expression
opeq2d  <. C ,  >.  <. C ,  >.

Proof of Theorem opeq2d
StepHypRef Expression
1 opeq1d.1 . 2
2 opeq2 3541 . 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:  fundmen  6222  recexnq  6374  elreal2  6688  frecuzrdgrrn  8835  frec2uzrdg  8836  frecuzrdgsuc  8842  iseqeq2  8855  iseqeq3  8856  iseqval  8860
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