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	|- ( ph -> P e. Prob )
	rrvvf.1	|- ( ph -> X e. ( rRndVar ` P ) )
Assertion	rrvrnss	|- ( ph -> ran X C_ RR )

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	frnd	|- ( ph -> ran X C_ RR )