Theorem salunid

Description: A set is an element of any sigma-algebra on it. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	salunid.1	⊢ ( 𝜑 → 𝑆 ∈ SAlg )
Assertion	salunid	⊢ ( 𝜑 → ∪ 𝑆 ∈ 𝑆 )

Proof

Step	Hyp	Ref	Expression
1		salunid.1	⊢ ( 𝜑 → 𝑆 ∈ SAlg )
2		saluni	⊢ ( 𝑆 ∈ SAlg → ∪ 𝑆 ∈ 𝑆 )
3	1 2	syl	⊢ ( 𝜑 → ∪ 𝑆 ∈ 𝑆 )