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Theorem opex 4080
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  |-  A  e. 
_V
opex.2  |-  B  e. 
_V
Assertion
Ref Expression
opex  |-  <. A ,  B >.  e.  _V

Proof of Theorem opex
StepHypRef Expression
1 opex.1 . 2  |-  A  e. 
_V
2 opex.2 . 2  |-  B  e. 
_V
3 opexg 4079 . 2  |-  ( ( A  e.  _V  /\  B  e.  _V )  -> 
<. A ,  B >.  e. 
_V )
41, 2, 3mp2an 418 1  |-  <. A ,  B >.  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1445   _Vcvv 2633   <.cop 3469
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-14 1457  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077  ax-sep 3978  ax-pow 4030  ax-pr 4060
This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-un 3017  df-in 3019  df-ss 3026  df-pw 3451  df-sn 3472  df-pr 3473  df-op 3475
This theorem is referenced by:  otth2  4092  opabid  4108  elopab  4109  opabm  4131  elvvv  4530  relsnop  4573  xpiindim  4604  raliunxp  4608  rexiunxp  4609  intirr  4851  xpmlem  4885  dmsnm  4930  dmsnopg  4936  cnvcnvsn  4941  op2ndb  4948  cnviinm  5006  funopg  5082  fsn  5508  fvsn  5531  idref  5574  oprabid  5719  dfoprab2  5734  rnoprab  5769  fo1st  5966  fo2nd  5967  eloprabi  6004  xporderlem  6034  cnvoprab  6037  dmtpos  6059  rntpos  6060  tpostpos  6067  iinerm  6404  th3qlem2  6435  elixpsn  6532  ensn1  6593  mapsnen  6608  xpsnen  6617  xpcomco  6622  xpassen  6626  xpmapenlem  6645  phplem2  6649  ac6sfi  6694  djuss  6841  genipdm  7172  ioof  9537  fsumcnv  10996
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