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Theorem opeq2i 4016
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 4013 . 2
31, 2ax-mp 5 1
Colors of variables: wff set class
Syntax hints:  =wceq 1654  <.cop 3844
This theorem is referenced by:  fnressn  5966  fressnfv  5968  seqomlem1  6756  recmulnq  8892  addresr  9064  seqval  11385  ids1  11802  wrdeqs1cat  11840  ressinbas  13576  oduval  14608  efgi0  15403  efgi1  15404  vrgpinv  15452  frgpnabllem1  15535  zlmval  16848  vdgr1c  21727  avril1  21808  ginvsn  21988  nvop  22217  phop  22370  wfrlem14  25655  swrdccat3a  28415  bnj601  29532  tgrpset  31782  erngset  31837  erngset-rN  31845
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3766  df-sn 3847  df-pr 3848  df-op 3850
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