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Theorem prid2g 3903
Description: An unordered pair contains its second member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by Stefan Allan, 8-Nov-2008.)
Assertion
Ref Expression
prid2g  |-  ( B  e.  V  ->  B  e.  { A ,  B } )

Proof of Theorem prid2g
StepHypRef Expression
1 prid1g 3902 . 2  |-  ( B  e.  V  ->  B  e.  { B ,  A } )
2 prcom 3874 . 2  |-  { B ,  A }  =  { A ,  B }
31, 2syl6eleq 2525 1  |-  ( B  e.  V  ->  B  e.  { A ,  B } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   {cpr 3807
This theorem is referenced by:  fr2nr  4552  unisn2  4702  pw2f1olem  7203  gcdcllem3  13001  indistopon  17053  pptbas  17060  coseq0negpitopi  20399  usgra2edg  21390  nb3graprlem1  21448  nb3graprlem2  21449  2trllemF  21537  vdgr1b  21663  prsiga  24502  pmtrprfv  27311  imarnf1pr  28015
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-sn 3812  df-pr 3813
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