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Theorem altopex 28130
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 28128 . 2  |-  << A ,  B >>  =  { { A } ,  { A ,  { B } } }
2 prex 4637 . 2  |-  { { A } ,  { A ,  { B } } }  e.  _V
31, 2eqeltri 2536 1  |-  << A ,  B >>  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758   _Vcvv 3072   {csn 3980   {cpr 3982   <<caltop 28126
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431  ax-sep 4516  ax-nul 4524  ax-pr 4634
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-ne 2647  df-v 3074  df-dif 3434  df-un 3436  df-nul 3741  df-sn 3981  df-pr 3983  df-altop 28128
This theorem is referenced by:  elaltxp  28145
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