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Theorem prid1 3682
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 3680 . 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 2136   _Vcvv 2726   {cpr 3577
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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147
This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583
This theorem is referenced by:  prid2  3683  prnz  3698  preqr1  3748  preq12b  3750  prel12  3751  opi1  4210  opeluu  4428  onsucelsucexmidlem1  4505  regexmidlem1  4510  reg2exmidlema  4511  opthreg  4533  ordtri2or2exmid  4548  ontri2orexmidim  4549  dmrnssfld  4867  funopg  5222  acexmidlemb  5834  0lt2o  6409  2dom  6771  unfiexmid  6883  djuss  7035  exmidomni  7106  exmidonfinlem  7149  exmidaclem  7164  reelprrecn  7888  pnfxr  7951  sup3exmid  8852  lgsdir2lem3  13571  bdop  13757  2o01f  13876  iswomni0  13930
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