Theorem rrvdm

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

	Ref	Expression
Hypotheses	isrrvv.1	|- ( ph -> P e. Prob )
	rrvvf.1	|- ( ph -> X e. ( rRndVar ` P ) )
Assertion	rrvdm	|- ( ph -> dom X = U. dom P )

Proof

Step	Hyp	Ref	Expression
1		isrrvv.1	|- ( ph -> P e. Prob )
2		rrvvf.1	|- ( ph -> X e. ( rRndVar ` P ) )
3	1 2	rrvvf	|- ( ph -> X : U. dom P --> RR )
4	3	fdmd	|- ( ph -> dom X = U. dom P )