Theorem elrpd

Description: Membership in the set of positive reals. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	elrpd.1	|- ( ph -> A e. RR )
	elrpd.2	|- ( ph -> 0 < A )
Assertion	elrpd	|- ( ph -> A e. RR+ )

Proof

Step	Hyp	Ref	Expression
1		elrpd.1	|- ( ph -> A e. RR )
2		elrpd.2	|- ( ph -> 0 < A )
3		elrp	|- ( A e. RR+ <-> ( A e. RR /\ 0 < A ) )
4	1 2 3	sylanbrc	|- ( ph -> A e. RR+ )