Theorem altopex 32067

Description: Alternative ordered pairs always exist. (Contributed by Scott Fenton, 22-Mar-2012.)

Assertion

Ref	Expression
altopex	|- << A , B >> e. _V

Proof of Theorem altopex

Step	Hyp	Ref	Expression
1		df-altop 32065	. 2 |- << A , B >> = { { A } , { A , { B } } }
2		prex 4909	. 2 |- { { A } , { A , { B } } } e. _V
3	1, 2	eqeltri 2697	1 |- << A , B >> e. _V

Syntax hints:   e. wcel 1990   _Vcvv 3200   {csn 4177   {cpr 4179   <<caltop 32063

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pr 4906

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577  df-un 3579  df-nul 3916  df-sn 4178  df-pr 4180  df-altop 32065

This theorem is referenced by:  elaltxp  32082