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Theorem opex 3936
Description: An ordered pair of sets is a set. (Contributed by Jim Kingdon, 24-Sep-2018.) (Revised by Mario Carneiro, 24-May-2019.)
Hypotheses
Ref Expression
opex.1  _V
opex.2  _V
Assertion
Ref Expression
opex  <. ,  >.  _V

Proof of Theorem opex
StepHypRef Expression
1 opex.1 . 2  _V
2 opex.2 . 2  _V
3 opexg 3934 . 2  _V  _V  <. ,  >.  _V
41, 2, 3mp2an 404 1  <. ,  >.  _V
Colors of variables: wff set class
Syntax hints:   wcel 1370   _Vcvv 2531   <.cop 3349
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 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-14 1382  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000  ax-sep 3845  ax-pow 3897  ax-pr 3914
This theorem depends on definitions:  df-bi 110  df-3an 873  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-un 2895  df-in 2897  df-ss 2904  df-pw 3332  df-sn 3352  df-pr 3353  df-op 3355
This theorem is referenced by:  opabid  3964  elopab  3965  opabm  3987  elvvv  4326  xpiindim  4396  raliunxp  4400  rexiunxp  4401  intirr  4634  xpmlem  4667  dmsnm  4709  dmsnopg  4715  cnvcnvsn  4720  cnviinm  4782  funopg  4856  fsn  5256  idref  5317  oprabid  5457  dfoprab2  5471  rnoprab  5506  fo1st  5703  fo2nd  5704  eloprabi  5741  xporderlem  5770  dmtpos  5789  rntpos  5790  tpostpos  5797  tfrlemi14  5865  iinerm  6085  th3qlem2  6116  genipdm  6364  genpelpw  6365
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