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Theorem prid2g 3733
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 3732 . 2  |-  ( B  e.  V  ->  B  e.  { B ,  A } )
2 prcom 3705 . 2  |-  { B ,  A }  =  { A ,  B }
31, 2syl6eleq 2373 1  |-  ( B  e.  V  ->  B  e.  { A ,  B } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   {cpr 3641
This theorem is referenced by:  fr2nr  4371  unisn2  4522  pw2f1olem  6966  gcdcllem3  12692  indistopon  16738  pptbas  16745  coseq0negpitopi  19871  prsiga  23492  vdgr1b  23895  fnckle  26045  pmtrprfv  27396
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-sn 3646  df-pr 3647
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