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Theorem altopex 34591
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 34589 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 prex 5390 . 2 {{𝐴}, {𝐴, {𝐵}}} ∈ V
31, 2eqeltri 2830 1 𝐴, 𝐵⟫ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3444  {csn 4587  {cpr 4589  caltop 34587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5257  ax-nul 5264  ax-pr 5385
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-dif 3914  df-un 3916  df-nul 4284  df-sn 4588  df-pr 4590  df-altop 34589
This theorem is referenced by:  elaltxp  34606
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