Metamath Proof Explorer


Theorem rrvdm

Description: The domain of a random variable is the universe. (Contributed by Thierry Arnoux, 25-Jan-2017)

Ref Expression
Hypotheses isrrvv.1 ( 𝜑𝑃 ∈ Prob )
rrvvf.1 ( 𝜑𝑋 ∈ ( rRndVar ‘ 𝑃 ) )
Assertion rrvdm ( 𝜑 → dom 𝑋 = dom 𝑃 )

Proof

Step Hyp Ref Expression
1 isrrvv.1 ( 𝜑𝑃 ∈ Prob )
2 rrvvf.1 ( 𝜑𝑋 ∈ ( rRndVar ‘ 𝑃 ) )
3 1 2 rrvvf ( 𝜑𝑋 : dom 𝑃 ⟶ ℝ )
4 3 fdmd ( 𝜑 → dom 𝑋 = dom 𝑃 )