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Theorem altopex 32394
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 32392 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 prex 5058 . 2 {{𝐴}, {𝐴, {𝐵}}} ∈ V
31, 2eqeltri 2835 1 𝐴, 𝐵⟫ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2139  Vcvv 3340  {csn 4321  {cpr 4323  caltop 32390
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pr 5055
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-dif 3718  df-un 3720  df-nul 4059  df-sn 4322  df-pr 4324  df-altop 32392
This theorem is referenced by:  elaltxp  32409
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