Theorem unexOLD 7723

Description: Obsolete version of unex 7722 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 4890	. 2 ⊢ ∪ {𝐴, 𝐵} = (𝐴 ∪ 𝐵)
4		prex 5394	. . 3 ⊢ {𝐴, 𝐵} ∈ V
5	4	uniex 7719	. 2 ⊢ ∪ {𝐴, 𝐵} ∈ V
6	3, 5	eqeltrri 2826	1 ⊢ (𝐴 ∪ 𝐵) ∈ V

Syntax hints:   ∈ wcel 2109  Vcvv 3450   ∪ cun 3914  {cpr 4593  ∪ cuni 4873

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 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702  ax-sep 5253  ax-nul 5263  ax-pr 5389  ax-un 7713

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-dif 3919  df-un 3921  df-ss 3933  df-nul 4299  df-sn 4592  df-pr 4594  df-uni 4874

This theorem is referenced by: (None)