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Theorem opex 3956
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 3954 . 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 3369
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-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3865  ax-pow 3917  ax-pr 3934
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 3352  df-sn 3372  df-pr 3373  df-op 3375
This theorem is referenced by:  opabid  3984  elopab  3985  opabm  4007  elvvv  4345  xpiindim  4415  raliunxp  4419  rexiunxp  4420  intirr  4653  xpmlem  4686  dmsnm  4728  dmsnopg  4734  cnvcnvsn  4739  cnviinm  4801  funopg  4875  fsn  5276  idref  5337  oprabid  5477  dfoprab2  5491  rnoprab  5526  fo1st  5723  fo2nd  5724  eloprabi  5761  xporderlem  5790  dmtpos  5809  rntpos  5810  tpostpos  5817  iinerm  6107  th3qlem2  6138  ensn1  6205  xpsnen  6224  xpcomco  6229  xpassen  6233  genipdm  6491  genpelpw  6492  ioof  8558
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