Theorem altopex 36452

Description: Alternative ordered pairs always exist. (Contributed by Scott Fenton, 22-Mar-2012.)

Assertion

Ref	Expression
altopex	⊢ ⟪𝐴, 𝐵⟫ ∈ V

Proof of Theorem altopex

Step	Hyp	Ref	Expression
1		df-altop 36450	. 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2		prex 5409	. 2 ⊢ {{𝐴}, {𝐴, {𝐵}}} ∈ V
3	1, 2	eqeltri 2859	1 ⊢ ⟪𝐴, 𝐵⟫ ∈ V

Syntax hints:   ∈ wcel 2143  Vcvv 3455  {csn 4589  {cpr 4591  ⟪caltop 36448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-sep 5257  ax-pr 5404

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-un 3910  df-sn 4590  df-pr 4592  df-altop 36450

This theorem is referenced by:  elaltxp  36467