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Theorem altopex 35941
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 35939 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 prex 5442 . 2 {{𝐴}, {𝐴, {𝐵}}} ∈ V
31, 2eqeltri 2834 1 𝐴, 𝐵⟫ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2105  Vcvv 3477  {csn 4630  {cpr 4632  caltop 35937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705  ax-sep 5301  ax-nul 5311  ax-pr 5437
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-dif 3965  df-un 3967  df-nul 4339  df-sn 4631  df-pr 4633  df-altop 35939
This theorem is referenced by:  elaltxp  35956
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