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Theorem opth2 4141
 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 4140 . 2
41, 2, 3mp2an 656 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1619   wcel 1621  cvv 2727  cop 3547 This theorem is referenced by:  eqvinop  4144  opelxp  4626  fsn  5548  opiota  6174  canthwe  8153  ltresr  8642  diblsmopel  30050  cdlemn7  30082  dihordlem7  30093  xihopellsmN  30133  dihopellsm  30134  dihpN  30215 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553
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