Metamath Proof Explorer


Theorem rrvrnss

Description: The range of a random variable as a subset of RR . (Contributed by Thierry Arnoux, 6-Feb-2017)

Ref Expression
Hypotheses isrrvv.1 φ P Prob
rrvvf.1 φ X RndVar P
Assertion rrvrnss φ ran X

Proof

Step Hyp Ref Expression
1 isrrvv.1 φ P Prob
2 rrvvf.1 φ X RndVar P
3 1 2 rrvvf φ X : dom P
4 3 frnd φ ran X