Metamath Proof Explorer


Theorem rrvfn

Description: A real-valued random variable is a function over the universe. (Contributed by Thierry Arnoux, 25-Jan-2017)

Ref Expression
Hypotheses isrrvv.1 φ P Prob
rrvvf.1 φ X RndVar P
Assertion rrvfn φ X Fn dom P

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 ffnd φ X Fn dom P