Metamath Proof Explorer

Theorem rpcnne0d

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

Ref Expression
Hypothesis rpred.1 
|- ( ph -> A e. RR+ )
Assertion rpcnne0d 
|- ( ph -> ( A e. CC /\ A =/= 0 ) )

Proof

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