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	$$⊢\phi \to S\in \mathrm{SAlg}$$
Assertion	salunid	$$⊢\phi \to \bigcup S\in S$$

Proof

Step	Hyp	Ref	Expression
1		salunid.1	$$⊢\phi \to S\in \mathrm{SAlg}$$
2		saluni	$$⊢S\in \mathrm{SAlg}\to \bigcup S\in S$$
3	1 2	syl	$$⊢\phi \to \bigcup S\in S$$