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Theorem altopex 25717
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 25715 . 2  |-  << A ,  B >>  =  { { A } ,  { A ,  { B } } }
2 prex 4374 . 2  |-  { { A } ,  { A ,  { B } } }  e.  _V
31, 2eqeltri 2482 1  |-  << A ,  B >>  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1721   _Vcvv 2924   {csn 3782   {cpr 3783   <<caltop 25713
This theorem is referenced by:  elaltxp  25732
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393  ax-sep 4298  ax-nul 4306  ax-pr 4371
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-v 2926  df-dif 3291  df-un 3293  df-nul 3597  df-sn 3788  df-pr 3789  df-altop 25715
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