Metamath Proof Explorer

Theorem rpne0d

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

Ref Expression
Hypothesis rpred.1 
|- ( ph -> A e. RR+ )
Assertion rpne0d 
|- ( ph -> A =/= 0 )

Proof

Step Hyp Ref Expression
1 rpred.1 
 |-  ( ph -> A e. RR+ )
2 rpne0 
 |-  ( A e. RR+ -> A =/= 0 )
3 1 2 syl 
 |-  ( ph -> A =/= 0 )