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Theorem opeq12i 4222
Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.) (Proof shortened by Eric Schmidt, 4-Apr-2007.)
Hypotheses
Ref Expression
opeq1i.1
opeq12i.2
Assertion
Ref Expression
opeq12i

Proof of Theorem opeq12i
StepHypRef Expression
1 opeq1i.1 . 2
2 opeq12i.2 . 2
3 opeq12 4219 . 2
41, 2, 3mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  <.cop 4035
This theorem is referenced by:  elxp6  6832  addcompq  9349  mulcompq  9351  addassnq  9357  mulassnq  9358  distrnq  9360  1lt2nq  9372  axi2m1  9557  om2uzrdg  12067  axlowdimlem6  24250  rngoi  25382  nvop2  25501  nvvop  25502  phop  25733  hhsssh  26185  isdrngo1  30359
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036
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