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Metamath Proof Explorer

Theorem vol0

Description: The measure of the empty set. (Contributed by Glauco Siliprandi, 11-Dec-2019)

		Ref	Expression
	Assertion	vol0	$⊢ vol (\emptyset) = 0$

Step	Hyp	Ref	Expression
1		0mbl	$⊢ \emptyset \in dom vol$
2		mblvol	$⊢ \emptyset \in dom vol \to vol (\emptyset) = {vol}^{*} (\emptyset)$
3	1 2	ax-mp	$⊢ vol (\emptyset) = {vol}^{*} (\emptyset)$
4		ovol0	$⊢ {vol}^{*} (\emptyset) = 0$
5	3 4	eqtri	$⊢ vol (\emptyset) = 0$