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Theorem prid2g 3734
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 3733 . 2  |-  ( B  e.  V  ->  B  e.  { B ,  A } )
2 prcom 3706 . 2  |-  { B ,  A }  =  { A ,  B }
31, 2syl6eleq 2374 1  |-  ( B  e.  V  ->  B  e.  { A ,  B } )
Colors of variables: wff set class
Syntax hints:    -> wi 6    e. wcel 1688   {cpr 3642
This theorem is referenced by:  fr2nr  4370  unisn2  4521  pw2f1olem  6961  gcdcllem3  12686  indistopon  16732  pptbas  16739  coseq0negpitopi  19865  vdgr1b  23299  fnckle  25444  pmtrprfv  26795
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648  ax-6 1707  ax-7 1712  ax-11 1719  ax-12 1869  ax-ext 2265
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1534  df-nf 1537  df-sb 1636  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-v 2791  df-un 3158  df-sn 3647  df-pr 3648
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