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Theorem prid2g 3524
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 3523 . 2  |-  ( B  e.  V  ->  B  e.  { B ,  A } )
2 prcom 3495 . 2  |-  { B ,  A }  =  { A ,  B }
31, 2syl6eleq 2177 1  |-  ( B  e.  V  ->  B  e.  { A ,  B } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1436   {cpr 3426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2616  df-un 2990  df-sn 3431  df-pr 3432
This theorem is referenced by:  en2lp  4336  en2eqpr  6553  maxleim  10479  maxabslemval  10482
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