Theorem rrvf2

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

	Ref	Expression
Hypotheses	isrrvv.1	|- ( ph -> P e. Prob )
	rrvvf.1	|- ( ph -> X e. ( rRndVar ` P ) )
Assertion	rrvf2	|- ( ph -> X : dom X --> 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	1 2	rrvdm	|- ( ph -> dom X = U. dom P )
5	4	feq2d	|- ( ph -> ( X : dom X --> RR <-> X : U. dom P --> RR ) )
6	3 5	mpbird	|- ( ph -> X : dom X --> RR )