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Theorem opex 3957
 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 3955 . 2 ((A V B V) → ⟨A, B V)
41, 2, 3mp2an 402 1 A, B V
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1390  Vcvv 2551  ⟨cop 3370 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376 This theorem is referenced by:  opabid  3985  elopab  3986  opabm  4008  elvvv  4346  xpiindim  4416  raliunxp  4420  rexiunxp  4421  intirr  4654  xpmlem  4687  dmsnm  4729  dmsnopg  4735  cnvcnvsn  4740  cnviinm  4802  funopg  4877  fsn  5278  idref  5339  oprabid  5480  dfoprab2  5494  rnoprab  5529  fo1st  5726  fo2nd  5727  eloprabi  5764  xporderlem  5793  dmtpos  5812  rntpos  5813  tpostpos  5820  iinerm  6114  th3qlem2  6145  ensn1  6212  xpsnen  6231  xpcomco  6236  xpassen  6240  genipdm  6499  ioof  8610
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