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Theorem prid2 3468
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 3467 . 2 B {B, A}
3 prcom 3437 . 2 {B, A} = {A, B}
42, 3eleqtri 2109 1 B {A, B}
Colors of variables: wff set class
Syntax hints:   wcel 1390  Vcvv 2551  {cpr 3368
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374
This theorem is referenced by:  prel12  3533  opi2  3961  opeluu  4148  onsucelsucexmid  4215  regexmidlemm  4217  dmrnssfld  4538  funopg  4877  acexmidlema  5446  acexmidlemcase  5450  acexmidlem2  5452  2dom  6221  cnelprrecn  6775  mnfxr  8424  m1expcl2  8891  bdop  9264
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