Theorem rprene0d

Description: A positive real is a nonzero real number. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	rpred.1	|- ( ph -> A e. RR+ )
Assertion	rprene0d	|- ( ph -> ( A e. RR /\ A =/= 0 ) )

Proof

Step	Hyp	Ref	Expression
1		rpred.1	|- ( ph -> A e. RR+ )
2	1	rpred	|- ( ph -> A e. RR )
3	1	rpne0d	|- ( ph -> A =/= 0 )
4	2 3	jca	|- ( ph -> ( A e. RR /\ A =/= 0 ) )