Theorem dmovnsal

Description: The domain of the Lebesgue measure is a sigma-algebra. (Contributed by Glauco Siliprandi, 24-Dec-2020)

	Ref	Expression
Hypotheses	dmovnsal.x	⊢ ( 𝜑 → 𝑋 ∈ Fin )
	dmovnsal.s	⊢ 𝑆 = dom ( voln ‘ 𝑋 )
Assertion	dmovnsal	⊢ ( 𝜑 → 𝑆 ∈ SAlg )

Proof

Step	Hyp	Ref	Expression
1		dmovnsal.x	⊢ ( 𝜑 → 𝑋 ∈ Fin )
2		dmovnsal.s	⊢ 𝑆 = dom ( voln ‘ 𝑋 )
3	1	vonmea	⊢ ( 𝜑 → ( voln ‘ 𝑋 ) ∈ Meas )
4	3 2	dmmeasal	⊢ ( 𝜑 → 𝑆 ∈ SAlg )