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Theorem opex 4231
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 4230 . 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 2148  Vcvv 2739  cop 3597
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-14 2151  ax-ext 2159  ax-sep 4123  ax-pow 4176  ax-pr 4211
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-un 3135  df-in 3137  df-ss 3144  df-pw 3579  df-sn 3600  df-pr 3601  df-op 3603
This theorem is referenced by:  otth2  4243  opabid  4259  elopab  4260  opabm  4282  elvvv  4691  relsnop  4734  xpiindim  4766  raliunxp  4770  rexiunxp  4771  intirr  5017  xpmlem  5051  dmsnm  5096  dmsnopg  5102  cnvcnvsn  5107  op2ndb  5114  cnviinm  5172  funopg  5252  fsn  5690  fvsn  5713  idref  5759  oprabid  5909  dfoprab2  5924  rnoprab  5960  fo1st  6160  fo2nd  6161  eloprabi  6199  xporderlem  6234  cnvoprab  6237  dmtpos  6259  rntpos  6260  tpostpos  6267  iinerm  6609  th3qlem2  6640  elixpsn  6737  ensn1  6798  mapsnen  6813  xpsnen  6823  xpcomco  6828  xpassen  6832  xpmapenlem  6851  phplem2  6855  ac6sfi  6900  djuss  7071  genipdm  7517  ioof  9973  fsumcnv  11447  fprodcnv  11635  prdsex  12723  txdis1cn  13817
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