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Theorem altopex 29184
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 29182 . 2  |-  << A ,  B >>  =  { { A } ,  { A ,  { B } } }
2 prex 4689 . 2  |-  { { A } ,  { A ,  { B } } }  e.  _V
31, 2eqeltri 2551 1  |-  << A ,  B >>  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1767   _Vcvv 3113   {csn 4027   {cpr 4029   <<caltop 29180
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-v 3115  df-dif 3479  df-un 3481  df-nul 3786  df-sn 4028  df-pr 4030  df-altop 29182
This theorem is referenced by:  elaltxp  29199
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