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Metamath Proof Explorer

Theorem unexOLD

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

	Ref	Expression
Hypotheses	unex.1	⊢ 𝐴 ∈ V
	unex.2	⊢ 𝐵 ∈ V
Assertion	unexOLD	⊢ ( 𝐴 ∪ 𝐵 ) ∈ V

Proof

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