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Theorem prid2g 3712
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 (𝐵𝑉𝐵 ∈ {𝐴, 𝐵})

Proof of Theorem prid2g
StepHypRef Expression
1 prid1g 3711 . 2 (𝐵𝑉𝐵 ∈ {𝐵, 𝐴})
2 prcom 3683 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
31, 2eleqtrdi 2282 1 (𝐵𝑉𝐵 ∈ {𝐴, 𝐵})
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2160  {cpr 3608
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614
This theorem is referenced by:  en2lp  4571  pw2f1odclem  6862  en2eqpr  6935  maxleim  11246  maxabslemval  11249  xrmaxleim  11284  xrmaxiflemval  11290  xrmaxaddlem  11300  2stropg  12632  2strop1g  12635  coseq0negpitopi  14717
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