Theorem snmbl

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

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

Proof

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