Theorem unexOLD 7678

Description: Obsolete version of unex 7677 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 4873	. 2 ⊢ ∪ {𝐴, 𝐵} = (𝐴 ∪ 𝐵)
4		prex 5373	. . 3 ⊢ {𝐴, 𝐵} ∈ V
5	4	uniex 7674	. 2 ⊢ ∪ {𝐴, 𝐵} ∈ V
6	3, 5	eqeltrri 2828	1 ⊢ (𝐴 ∪ 𝐵) ∈ V

Syntax hints:   ∈ wcel 2111  Vcvv 3436   ∪ cun 3895  {cpr 4575  ∪ cuni 4856

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 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-sep 5232  ax-nul 5242  ax-pr 5368  ax-un 7668

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-dif 3900  df-un 3902  df-ss 3914  df-nul 4281  df-sn 4574  df-pr 4576  df-uni 4857

This theorem is referenced by: (None)