Theorem ovolsn

Description: A singleton has 0 outer Lebesgue measure. (Contributed by Mario Carneiro, 15-Aug-2014)

	Ref	Expression
Assertion	ovolsn	$$⊢A\in ℝ\to {vol}^{*}\left(\left\{A\right\}\right)=0$$

Proof

Step	Hyp	Ref	Expression
1		snfi	$$⊢\left\{A\right\}\in \mathrm{Fin}$$
2		snssi	$$⊢A\in ℝ\to \left\{A\right\}\subseteq ℝ$$
3		ovolfi	$$⊢\left(\left\{A\right\}\in \mathrm{Fin}\wedge \left\{A\right\}\subseteq ℝ\right)\to {vol}^{*}\left(\left\{A\right\}\right)=0$$
4	1 2 3	sylancr	$$⊢A\in ℝ\to {vol}^{*}\left(\left\{A\right\}\right)=0$$