Theorem unexOLD 7692

Description: Obsolete version of unex 7691 as of 21-Jul-2025. (Contributed by NM, 1-Jul-1994.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
unex.1	⊢ 𝐴 ∈ V
unex.2	⊢ 𝐵 ∈ V

Assertion

Ref	Expression
unexOLD	⊢ (𝐴 ∪ 𝐵) ∈ V

Proof of Theorem unexOLD

Step	Hyp	Ref	Expression
1		unex.1	. . 3 ⊢ 𝐴 ∈ V
2		unex.2	. . 3 ⊢ 𝐵 ∈ V
3	1, 2	unipr 4881	. 2 ⊢ ∪ {𝐴, 𝐵} = (𝐴 ∪ 𝐵)
4		prex 5383	. . 3 ⊢ {𝐴, 𝐵} ∈ V
5	4	uniex 7688	. 2 ⊢ ∪ {𝐴, 𝐵} ∈ V
6	3, 5	eqeltrri 2834	1 ⊢ (𝐴 ∪ 𝐵) ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3441   ∪ cun 3900  {cpr 4583  ∪ cuni 4864

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5242  ax-nul 5252  ax-pr 5378  ax-un 7682

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3443  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4287  df-sn 4582  df-pr 4584  df-uni 4865

This theorem is referenced by: (None)