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Theorem altopex 30285
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 30283 . 2  |-  << A ,  B >>  =  { { A } ,  { A ,  { B } } }
2 prex 4632 . 2  |-  { { A } ,  { A ,  { B } } }  e.  _V
31, 2eqeltri 2486 1  |-  << A ,  B >>  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1842   _Vcvv 3058   {csn 3971   {cpr 3973   <<caltop 30281
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4516  ax-nul 4524  ax-pr 4629
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-v 3060  df-dif 3416  df-un 3418  df-nul 3738  df-sn 3972  df-pr 3974  df-altop 30283
This theorem is referenced by:  elaltxp  30300
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