Theorem pri2 2455

Description: One of the two elements of an unordered pair. Part of Theorem 7.6 of [Quine] p. 49.

Hypothesis

Ref	Expression
pri2.1	|- B e. V

Assertion

Ref	Expression
pri2	|- B e. {A, B}

Proof of Theorem pri2

Step	Hyp	Ref	Expression
1		pri2.1	. . 3 |- B e. V
2	1	pri1 2454	. 2 |- B e. {B, A}
3		prcom 2451	. 2 |- {B, A} = {A, B}
4	2, 3	eleqtr 1549	1 |- B e. {A, B}

Syntax hints:   e. wcel 960  Vcvv 1814  {cpr 2414

This theorem is referenced by:  tpi2 2460  prss 2475  prel12 2488  opi2 2791  opthwiener 2813  opeluu 2885  fr2nr 2931  dmrnssfld 3363  funopg 3553  2dom 4433  pw2en 4452  aceq6b 4752  brdom7disj 4814  brdom6disj 4815  mnfxr 5506  indistop 7645

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053  df-sn 2416  df-pr 2417

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