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Theorem prid2g 3515
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 3514 . 2 (𝐵𝑉𝐵 ∈ {𝐵, 𝐴})
2 prcom 3486 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
31, 2syl6eleq 2175 1 (𝐵𝑉𝐵 ∈ {𝐴, 𝐵})
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1434  {cpr 3417
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-sn 3422  df-pr 3423
This theorem is referenced by:  en2lp  4325  en2eqpr  6458  maxleim  10292  maxabslemval  10295
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