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Theorem opelvv 4333
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  _V
opelvv.2  _V
Assertion
Ref Expression
opelvv  <. ,  >.  _V 
X.  _V

Proof of Theorem opelvv
StepHypRef Expression
1 opelvv.1 . 2  _V
2 opelvv.2 . 2  _V
3 opelxpi 4319 . 2  _V  _V  <. ,  >.  _V  X.  _V
41, 2, 3mp2an 402 1  <. ,  >.  _V 
X.  _V
Colors of variables: wff set class
Syntax hints:   wcel 1390   _Vcvv 2551   <.cop 3370    X. cxp 4286
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-opab 3810  df-xp 4294
This theorem is referenced by:  relsnop  4387  relopabi  4406  eqop2  5746
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