Metamath Proof Explorer


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 ) )