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

Theorem altopex 24494
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 24492 . 2  |-  << A ,  B >>  =  { { A } ,  { A ,  { B } } }
2 prex 4217 . 2  |-  { { A } ,  { A ,  { B } } }  e.  _V
31, 2eqeltri 2353 1  |-  << A ,  B >>  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   _Vcvv 2788   {csn 3640   {cpr 3641   <<caltop 24490
This theorem is referenced by:  elaltxp  24509
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-nul 3456  df-sn 3646  df-pr 3647  df-altop 24492
  Copyright terms: Public domain W3C validator