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Theorem opex 3994
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  e. 
_V
opex.2  |-  B  e. 
_V
Assertion
Ref Expression
opex  |-  <. A ,  B >.  e.  _V

Proof of Theorem opex
StepHypRef Expression
1 opex.1 . 2  |-  A  e. 
_V
2 opex.2 . 2  |-  B  e. 
_V
3 opexg 3992 . 2  |-  ( ( A  e.  _V  /\  B  e.  _V )  -> 
<. A ,  B >.  e. 
_V )
41, 2, 3mp2an 410 1  |-  <. A ,  B >.  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1409   _Vcvv 2574   <.cop 3406
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955  ax-pr 3972
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-pw 3389  df-sn 3409  df-pr 3410  df-op 3412
This theorem is referenced by:  opabid  4022  elopab  4023  opabm  4045  elvvv  4431  xpiindim  4501  raliunxp  4505  rexiunxp  4506  intirr  4739  xpmlem  4772  dmsnm  4814  dmsnopg  4820  cnvcnvsn  4825  cnviinm  4887  funopg  4962  fsn  5363  idref  5424  oprabid  5565  dfoprab2  5580  rnoprab  5615  fo1st  5812  fo2nd  5813  eloprabi  5850  xporderlem  5880  cnvoprab  5883  dmtpos  5902  rntpos  5903  tpostpos  5910  iinerm  6209  th3qlem2  6240  ensn1  6307  xpsnen  6326  xpcomco  6331  xpassen  6335  phplem2  6347  ac6sfi  6383  genipdm  6672  ioof  8941
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