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Theorem prid2g 3530
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 3529 . 2 (𝐵𝑉𝐵 ∈ {𝐵, 𝐴})
2 prcom 3501 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
31, 2syl6eleq 2177 1 (𝐵𝑉𝐵 ∈ {𝐴, 𝐵})
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1436  {cpr 3432
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 2617  df-un 2992  df-sn 3437  df-pr 3438
This theorem is referenced by:  en2lp  4343  en2eqpr  6575  maxleim  10534  maxabslemval  10537
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