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Theorem opelvv 4924
 Description: Ordered pair membership in the universal class of ordered pairs. (Contributed by NM, 22-Aug-2013.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
opelvv.1
opelvv.2
Assertion
Ref Expression
opelvv

Proof of Theorem opelvv
StepHypRef Expression
1 opelvv.1 . 2
2 opelvv.2 . 2
3 opelxpi 4910 . 2
41, 2, 3mp2an 654 1
 Colors of variables: wff set class Syntax hints:   wcel 1725  cvv 2956  cop 3817   cxp 4876 This theorem is referenced by:  relsnop  4980  relopabi  5000  1st2ndb  6387  eqop2  6390  evlfcl  14319  brtxp  25725  brpprod  25730  brsset  25734  brcart  25777  brcup  25784  brcap  25785 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-opab 4267  df-xp 4884
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