Theorem unexOLD 7691

Description: Obsolete version of unex 7690 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 4857	. 2 ⊢ ∪ {𝐴, 𝐵} = (𝐴 ∪ 𝐵)
4		prex 5369	. . 3 ⊢ {𝐴, 𝐵} ∈ V
5	4	uniex 7687	. 2 ⊢ ∪ {𝐴, 𝐵} ∈ V
6	3, 5	eqeltrri 2838	1 ⊢ (𝐴 ∪ 𝐵) ∈ V

Syntax hints:   ∈ wcel 2121  Vcvv 3433   ∪ cun 3882  {cpr 4559  ∪ cuni 4840

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-ext 2713  ax-sep 5220  ax-pr 5364  ax-un 7681

This theorem depends on definitions:  df-bi 209  df-an 398  df-or 855  df-tru 1551  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-v 3435  df-un 3889  df-ss 3901  df-sn 4558  df-pr 4560  df-uni 4841

This theorem is referenced by: (None)