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Theorem opex 4121
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 4120 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → ⟨𝐴, 𝐵⟩ ∈ V)
41, 2, 3mp2an 422 1 𝐴, 𝐵⟩ ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1465  Vcvv 2660  cop 3500
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-pow 4068  ax-pr 4101
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-pw 3482  df-sn 3503  df-pr 3504  df-op 3506
This theorem is referenced by:  otth2  4133  opabid  4149  elopab  4150  opabm  4172  elvvv  4572  relsnop  4615  xpiindim  4646  raliunxp  4650  rexiunxp  4651  intirr  4895  xpmlem  4929  dmsnm  4974  dmsnopg  4980  cnvcnvsn  4985  op2ndb  4992  cnviinm  5050  funopg  5127  fsn  5560  fvsn  5583  idref  5626  oprabid  5771  dfoprab2  5786  rnoprab  5822  fo1st  6023  fo2nd  6024  eloprabi  6062  xporderlem  6096  cnvoprab  6099  dmtpos  6121  rntpos  6122  tpostpos  6129  iinerm  6469  th3qlem2  6500  elixpsn  6597  ensn1  6658  mapsnen  6673  xpsnen  6683  xpcomco  6688  xpassen  6692  xpmapenlem  6711  phplem2  6715  ac6sfi  6760  djuss  6923  genipdm  7292  ioof  9722  fsumcnv  11174  txdis1cn  12374
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