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Theorem prid1 3697
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 3695 . 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 2148   _Vcvv 2737   {cpr 3592
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-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-sn 3597  df-pr 3598
This theorem is referenced by:  prid2  3698  prnz  3713  preqr1  3766  preq12b  3768  prel12  3769  opi1  4228  opeluu  4446  onsucelsucexmidlem1  4523  regexmidlem1  4528  reg2exmidlema  4529  opthreg  4551  ordtri2or2exmid  4566  ontri2orexmidim  4567  dmrnssfld  4885  funopg  5245  acexmidlemb  5860  0lt2o  6435  2dom  6798  unfiexmid  6910  djuss  7062  exmidomni  7133  exmidonfinlem  7185  exmidaclem  7200  reelprrecn  7924  pnfxr  7987  sup3exmid  8890  lgsdir2lem3  14064  bdop  14249  2o01f  14368  iswomni0  14422
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