Theorem uniexd

Description: Deduction version of the ZF Axiom of Union in class notation. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	uniexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
Assertion	uniexd	⊢ ( 𝜑 → ∪ 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		uniexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		uniexg	⊢ ( 𝐴 ∈ 𝑉 → ∪ 𝐴 ∈ V )
3	1 2	syl	⊢ ( 𝜑 → ∪ 𝐴 ∈ V )