Theorem meacl

Description: The measure of a set is a nonnegative extended real. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypotheses	meacl.1	|- ( ph -> M e. Meas )
	meacl.2	|- S = dom M
	meacl.3	|- ( ph -> A e. S )
Assertion	meacl	|- ( ph -> ( M ` A ) e. ( 0 [,] +oo ) )

Proof

Step	Hyp	Ref	Expression
1		meacl.1	|- ( ph -> M e. Meas )
2		meacl.2	|- S = dom M
3		meacl.3	|- ( ph -> A e. S )
4	1 2	meaf	|- ( ph -> M : S --> ( 0 [,] +oo ) )
5	4 3	ffvelcdmd	|- ( ph -> ( M ` A ) e. ( 0 [,] +oo ) )