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Theorem altopex 31706
Description: Alternative ordered pairs always exist. (Contributed by Scott Fenton, 22-Mar-2012.)
Assertion
Ref Expression
altopex 𝐴, 𝐵⟫ ∈ V

Proof of Theorem altopex
StepHypRef Expression
1 df-altop 31704 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 prex 4870 . 2 {{𝐴}, {𝐴, {𝐵}}} ∈ V
31, 2eqeltri 2694 1 𝐴, 𝐵⟫ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 1987  Vcvv 3186  {csn 4148  {cpr 4150  caltop 31702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pr 4867
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-dif 3558  df-un 3560  df-nul 3892  df-sn 4149  df-pr 4151  df-altop 31704
This theorem is referenced by:  elaltxp  31721
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