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Theorem prid2 3451
Description: An unordered pair contains its second member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
prid2.1 B V
Assertion
Ref Expression
prid2 B {A, B}

Proof of Theorem prid2
StepHypRef Expression
1 prid2.1 . . 3 B V
21prid1 3450 . 2 B {B, A}
3 prcom 3420 . 2 {B, A} = {A, B}
42, 3eleqtri 2094 1 B {A, B}
Colors of variables: wff set class
Syntax hints:   wcel 1374  Vcvv 2535  {cpr 3351
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899  df-sn 3356  df-pr 3357
This theorem is referenced by:  prel12  3516  opi2  3944  opeluu  4132  onsucelsucexmid  4199  regexmidlemm  4201  dmrnssfld  4522  funopg  4860  acexmidlema  5427  acexmidlemcase  5431  acexmidlem2  5433  cnelprrecn  6619  bdop  7102
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