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Theorem prid2g 3746
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 3745 . 2  |-  ( B  e.  V  ->  B  e.  { B ,  A } )
2 prcom 3718 . 2  |-  { B ,  A }  =  { A ,  B }
31, 2syl6eleq 2386 1  |-  ( B  e.  V  ->  B  e.  { A ,  B } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   {cpr 3654
This theorem is referenced by:  fr2nr  4387  unisn2  4538  pw2f1olem  6982  gcdcllem3  12708  indistopon  16754  pptbas  16761  coseq0negpitopi  19887  prsiga  23507  vdgr1b  23910  fnckle  26148  pmtrprfv  27499  nb3graprlem1  28287  nb3graprlem2  28288
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-pr 3660
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