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Theorem prid1g 3636
Description: An unordered pair contains its first member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by Stefan Allan, 8-Nov-2008.)
Assertion
Ref Expression
prid1g  |-  ( A  e.  V  ->  A  e.  { A ,  B } )

Proof of Theorem prid1g
StepHypRef Expression
1 eqid 2253 . . 3  |-  A  =  A
21orci 381 . 2  |-  ( A  =  A  \/  A  =  B )
3 elprg 3561 . 2  |-  ( A  e.  V  ->  ( A  e.  { A ,  B }  <->  ( A  =  A  \/  A  =  B ) ) )
42, 3mpbiri 226 1  |-  ( A  e.  V  ->  A  e.  { A ,  B } )
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359    = wceq 1619    e. wcel 1621   {cpr 3545
This theorem is referenced by:  prid2g  3637  prid1  3638  opth1  4137  fr2nr  4264  fveqf1o  5658  pw2f1olem  6851  gcdcllem3  12566  pptbas  16577  coseq0negpitopi  19703  vdgr1b  23066  fnckle  25211  kelac2  26329  pmtrprfv  26562
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083  df-sn 3550  df-pr 3551
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