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Theorem prid2g 3826
 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 VB {A, B})

Proof of Theorem prid2g
StepHypRef Expression
1 prid1g 3825 . 2 (B VB {B, A})
2 prcom 3798 . 2 {B, A} = {A, B}
31, 2syl6eleq 2443 1 (B VB {A, B})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710  {cpr 3738 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742 This theorem is referenced by: (None)
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