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Theorem altopex 35961
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 35959 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 prex 5437 . 2 {{𝐴}, {𝐴, {𝐵}}} ∈ V
31, 2eqeltri 2837 1 𝐴, 𝐵⟫ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  Vcvv 3480  {csn 4626  {cpr 4628  caltop 35957
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-dif 3954  df-un 3956  df-nul 4334  df-sn 4627  df-pr 4629  df-altop 35959
This theorem is referenced by:  elaltxp  35976
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