Theorem unexd

Description: The union of two sets is a set. (Contributed by SN, 16-Jul-2024)

	Ref	Expression
Hypotheses	unexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
	unexd.2	⊢ ( 𝜑 → 𝐵 ∈ 𝑊 )
Assertion	unexd	⊢ ( 𝜑 → ( 𝐴 ∪ 𝐵 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		unexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		unexd.2	⊢ ( 𝜑 → 𝐵 ∈ 𝑊 )
3		unexg	⊢ ( ( 𝐴 ∈ 𝑉 ∧ 𝐵 ∈ 𝑊 ) → ( 𝐴 ∪ 𝐵 ) ∈ V )
4	1 2 3	syl2anc	⊢ ( 𝜑 → ( 𝐴 ∪ 𝐵 ) ∈ V )