Theorem pri2 1842

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 ∈ V

Assertion

Ref	Expression
pri2	⊢ B ∈ {A, B}

Proof of Theorem pri2

Step	Hyp	Ref	Expression
1		pri2.1	. . 3 ⊢ B ∈ V
2	1	pri1 1841	. 2 ⊢ B ∈ {B, A}
3		prcom 1840	. 2 ⊢ {B, A} = {A, B}
4	2, 3	eleqtr 1161	1 ⊢ B ∈ {A, B}

Syntax hints:   ∈ wcel 1092  Vcvv 1348  {cpr 1809

This theorem is referenced by:  tpi2 1844  prss 1854  prel12 1875  opi2 1896  opthwiener 1914  opeluu 1953  fr2nr 2177  2dom 3332  pw2en 3348  aceq6b 3565

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-sn 1811  df-pr 1812

metamath.org