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Theorem opex 4019
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 ∈ V
opex.2 𝐵 ∈ V
Assertion
Ref Expression
opex 𝐴, 𝐵⟩ ∈ V

Proof of Theorem opex
StepHypRef Expression
1 opex.1 . 2 𝐴 ∈ V
2 opex.2 . 2 𝐵 ∈ V
3 opexg 4018 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → ⟨𝐴, 𝐵⟩ ∈ V)
41, 2, 3mp2an 417 1 𝐴, 𝐵⟩ ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1434  Vcvv 2612  cop 3425
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3922  ax-pow 3974  ax-pr 3999
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-un 2988  df-in 2990  df-ss 2997  df-pw 3408  df-sn 3428  df-pr 3429  df-op 3431
This theorem is referenced by:  otth2  4031  opabid  4047  elopab  4048  opabm  4070  elvvv  4458  relsnop  4501  xpiindim  4530  raliunxp  4534  rexiunxp  4535  intirr  4772  xpmlem  4805  dmsnm  4849  dmsnopg  4855  cnvcnvsn  4860  op2ndb  4867  cnviinm  4925  funopg  5000  fsn  5410  fvsn  5433  idref  5475  oprabid  5615  dfoprab2  5630  rnoprab  5665  fo1st  5862  fo2nd  5863  eloprabi  5900  xporderlem  5930  cnvoprab  5933  dmtpos  5952  rntpos  5953  tpostpos  5960  iinerm  6293  th3qlem2  6324  ensn1  6442  mapsnen  6457  xpsnen  6466  xpcomco  6471  xpassen  6475  xpmapenlem  6494  phplem2  6498  ac6sfi  6543  djuss  6667  genipdm  6977  ioof  9283
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