Metamath Proof Explorer


Theorem dmvon

Description: Lebesgue measurable n-dimensional subsets of Reals. (Contributed by Glauco Siliprandi, 24-Dec-2020)

Ref Expression
Hypothesis dmvon.x φ X Fin
Assertion dmvon φ dom voln X = CaraGen voln* X

Proof

Step Hyp Ref Expression
1 dmvon.x φ X Fin
2 1 vonval φ voln X = voln* X CaraGen voln* X
3 2 dmeqd φ dom voln X = dom voln* X CaraGen voln* X
4 1 ovnome φ voln* X OutMeas
5 eqid CaraGen voln* X = CaraGen voln* X
6 5 caragenss voln* X OutMeas CaraGen voln* X dom voln* X
7 4 6 syl φ CaraGen voln* X dom voln* X
8 ssdmres CaraGen voln* X dom voln* X dom voln* X CaraGen voln* X = CaraGen voln* X
9 7 8 sylib φ dom voln* X CaraGen voln* X = CaraGen voln* X
10 eqidd φ CaraGen voln* X = CaraGen voln* X
11 3 9 10 3eqtrd φ dom voln X = CaraGen voln* X