Theorem rpregt0d

Description: A positive real is real and greater than zero. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	rpred.1	|- ( ph -> A e. RR+ )
Assertion	rpregt0d	|- ( ph -> ( A e. RR /\ 0 < A ) )

Proof

Step	Hyp	Ref	Expression
1		rpred.1	|- ( ph -> A e. RR+ )
2	1	rpred	|- ( ph -> A e. RR )
3	1	rpgt0d	|- ( ph -> 0 < A )
4	2 3	jca	|- ( ph -> ( A e. RR /\ 0 < A ) )