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Theorem opth2 4730
Description: Ordered pair theorem. (Contributed by NM, 21-Sep-2014.)
Hypotheses
Ref Expression
opth2.1
opth2.2
Assertion
Ref Expression
opth2

Proof of Theorem opth2
StepHypRef Expression
1 opth2.1 . 2
2 opth2.2 . 2
3 opthg2 4729 . 2
41, 2, 3mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818   cvv 3109  <.cop 4035
This theorem is referenced by:  eqvinop  4736  opelxp  5034  fsn  6069  opiota  6859  canthwe  9050  ltresr  9538  mat1dimelbas  18973  fmucndlem  20794  diblsmopel  36898  cdlemn7  36930  dihordlem7  36941  xihopellsmN  36981  dihopellsm  36982  dihpN  37063
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
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-ne 2654  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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