Theorem snmbl

Description: A singleton is measurable. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Assertion	snmbl	|- ( A e. RR -> { A } e. dom vol )

Proof

Step	Hyp	Ref	Expression
1		snssi	|- ( A e. RR -> { A } C_ RR )
2		ovolsn	|- ( A e. RR -> ( vol* ` { A } ) = 0 )
3		nulmbl	|- ( ( { A } C_ RR /\ ( vol* ` { A } ) = 0 ) -> { A } e. dom vol )
4	1 2 3	syl2anc	|- ( A e. RR -> { A } e. dom vol )