Theorem altopex 35236

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 35234	. 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2		prex 5431	. 2 ⊢ {{𝐴}, {𝐴, {𝐵}}} ∈ V
3	1, 2	eqeltri 2827	1 ⊢ ⟪𝐴, 𝐵⟫ ∈ V

Syntax hints:   ∈ wcel 2104  Vcvv 3472  {csn 4627  {cpr 4629  ⟪caltop 35232

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 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701  ax-sep 5298  ax-nul 5305  ax-pr 5426

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 844  df-tru 1542  df-fal 1552  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2722  df-clel 2808  df-v 3474  df-dif 3950  df-un 3952  df-nul 4322  df-sn 4628  df-pr 4630  df-altop 35234

This theorem is referenced by:  elaltxp  35251