Theorem 0sald

Description: The empty set belongs to every sigma-algebra. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	0sald.1	$$⊢\phi \to S\in \mathrm{SAlg}$$
Assertion	0sald	$$⊢\phi \to \varnothing \in S$$

Proof

Step	Hyp	Ref	Expression
1		0sald.1	$$⊢\phi \to S\in \mathrm{SAlg}$$
2		0sal	$$⊢S\in \mathrm{SAlg}\to \varnothing \in S$$
3	1 2	syl	$$⊢\phi \to \varnothing \in S$$