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Theorem prid1 3599
Description: An unordered pair contains its first member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
prid1.1  |-  A  e. 
_V
Assertion
Ref Expression
prid1  |-  A  e. 
{ A ,  B }

Proof of Theorem prid1
StepHypRef Expression
1 prid1.1 . 2  |-  A  e. 
_V
2 prid1g 3597 . 2  |-  ( A  e.  _V  ->  A  e.  { A ,  B } )
31, 2ax-mp 5 1  |-  A  e. 
{ A ,  B }
Colors of variables: wff set class
Syntax hints:    e. wcel 1465   _Vcvv 2660   {cpr 3498
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504
This theorem is referenced by:  prid2  3600  prnz  3615  preqr1  3665  preq12b  3667  prel12  3668  opi1  4124  opeluu  4341  onsucelsucexmidlem1  4413  regexmidlem1  4418  reg2exmidlema  4419  opthreg  4441  ordtri2or2exmid  4456  dmrnssfld  4772  funopg  5127  acexmidlemb  5734  0lt2o  6306  2dom  6667  unfiexmid  6774  djuss  6923  exmidomni  6982  exmidonfinlem  7017  exmidaclem  7032  reelprrecn  7723  pnfxr  7786  sup3exmid  8683  bdop  13000  isomninnlem  13152
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