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Theorem prid2g 3696
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 3695 . 2 (𝐵𝑉𝐵 ∈ {𝐵, 𝐴})
2 prcom 3667 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
31, 2eleqtrdi 2270 1 (𝐵𝑉𝐵 ∈ {𝐴, 𝐵})
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2148  {cpr 3592
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-sn 3597  df-pr 3598
This theorem is referenced by:  en2lp  4550  en2eqpr  6901  maxleim  11195  maxabslemval  11198  xrmaxleim  11233  xrmaxiflemval  11239  xrmaxaddlem  11249  2stropg  12555  2strop1g  12558  coseq0negpitopi  13917
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