Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  altopex Unicode version

Theorem altopex 25053
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
StepHypRef Expression
1 df-altop 25051 . 2  |-  << A ,  B >>  =  { { A } ,  { A ,  { B } } }
2 prex 4296 . 2  |-  { { A } ,  { A ,  { B } } }  e.  _V
31, 2eqeltri 2428 1  |-  << A ,  B >>  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1710   _Vcvv 2864   {csn 3716   {cpr 3717   <<caltop 25049
This theorem is referenced by:  elaltxp  25068
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4220  ax-nul 4228  ax-pr 4293
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-v 2866  df-dif 3231  df-un 3233  df-nul 3532  df-sn 3722  df-pr 3723  df-altop 25051
  Copyright terms: Public domain W3C validator