Theorem 0sald

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

	Ref	Expression
Hypothesis	0sald.1	⊢ ( 𝜑 → 𝑆 ∈ SAlg )
Assertion	0sald	⊢ ( 𝜑 → ∅ ∈ 𝑆 )

Proof

Step	Hyp	Ref	Expression
1		0sald.1	⊢ ( 𝜑 → 𝑆 ∈ SAlg )
2		0sal	⊢ ( 𝑆 ∈ SAlg → ∅ ∈ 𝑆 )
3	1 2	syl	⊢ ( 𝜑 → ∅ ∈ 𝑆 )