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Theorem opex 4247
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 4246 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → ⟨𝐴, 𝐵⟩ ∈ V)
41, 2, 3mp2an 426 1 𝐴, 𝐵⟩ ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 2160  Vcvv 2752  cop 3610
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4192  ax-pr 4227
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616
This theorem is referenced by:  otth2  4259  opabid  4275  elopab  4276  opabm  4298  elvvv  4707  relsnop  4750  xpiindim  4782  raliunxp  4786  rexiunxp  4787  intirr  5033  xpmlem  5067  dmsnm  5112  dmsnopg  5118  cnvcnvsn  5123  op2ndb  5130  cnviinm  5188  funopg  5269  fsn  5708  fvsn  5731  idref  5777  oprabid  5927  dfoprab2  5942  rnoprab  5978  fo1st  6181  fo2nd  6182  eloprabi  6220  xporderlem  6255  cnvoprab  6258  dmtpos  6280  rntpos  6281  tpostpos  6288  iinerm  6632  th3qlem2  6663  elixpsn  6760  ensn1  6821  mapsnen  6836  xpsnen  6846  xpcomco  6851  xpassen  6855  xpmapenlem  6876  phplem2  6880  ac6sfi  6925  djuss  7098  genipdm  7544  ioof  10000  fsumcnv  11476  fprodcnv  11664  prdsex  12771  txdis1cn  14230
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