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Theorem prid2g 3664
 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 3663 . 2 (𝐵𝑉𝐵 ∈ {𝐵, 𝐴})
2 prcom 3635 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
31, 2eleqtrdi 2250 1 (𝐵𝑉𝐵 ∈ {𝐴, 𝐵})
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 2128  {cpr 3561 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567 This theorem is referenced by:  en2lp  4512  en2eqpr  6849  maxleim  11098  maxabslemval  11101  xrmaxleim  11134  xrmaxiflemval  11140  xrmaxaddlem  11150  2stropg  12263  2strop1g  12266  coseq0negpitopi  13128
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