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Theorem opeq2i 3980
Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.)
Hypothesis
Ref Expression
opeq1i.1
Assertion
Ref Expression
opeq2i

Proof of Theorem opeq2i
StepHypRef Expression
1 opeq1i.1 . 2
2 opeq2 3977 . 2
31, 2ax-mp 8 1
Colors of variables: wff set class
Syntax hints:  =wceq 1652  <.cop 3809
This theorem is referenced by:  fnressn  5910  fressnfv  5912  seqomlem1  6699  recmulnq  8833  addresr  9005  seqval  11326  ids1  11743  wrdeqs1cat  11781  ressinbas  13517  oduval  14549  efgi0  15344  efgi1  15345  vrgpinv  15393  frgpnabllem1  15476  zlmval  16789  vdgr1c  21668  avril1  21749  ginvsn  21929  nvop  22158  phop  22311  wfrlem14  25543  swrdccat3a  28183  bnj601  29228  tgrpset  31479  erngset  31534  erngset-rN  31542
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
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