Theorem altopex 33423

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 33421	. 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2		prex 5335	. 2 ⊢ {{𝐴}, {𝐴, {𝐵}}} ∈ V
3	1, 2	eqeltri 2911	1 ⊢ ⟪𝐴, 𝐵⟫ ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3496  {csn 4569  {cpr 4571  ⟪caltop 33419

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2795  ax-sep 5205  ax-nul 5212  ax-pr 5332

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2802  df-cleq 2816  df-clel 2895  df-nfc 2965  df-v 3498  df-dif 3941  df-un 3943  df-nul 4294  df-sn 4570  df-pr 4572  df-altop 33421

This theorem is referenced by:  elaltxp  33438