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Metamath Proof Explorer

Theorem snmbl

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

		Ref	Expression
	Assertion	snmbl	$⊢ A \in ℝ \to \{A\} \in dom vol$

Step	Hyp	Ref	Expression
1		snssi	$⊢ A \in ℝ \to \{A\} \subseteq ℝ$
2		ovolsn	$⊢ A \in ℝ \to {vol}^{*} (\{A\}) = 0$
3		nulmbl	$⊢ (\{A\} \subseteq ℝ \land {vol}^{*} (\{A\}) = 0) \to \{A\} \in dom vol$
4	1 2 3	syl2anc	$⊢ A \in ℝ \to \{A\} \in dom vol$