Metamath Proof Explorer

Theorem rpcnne0

Description: A positive real is a nonzero complex number. (Contributed by NM, 11-Nov-2008)

Ref Expression
Assertion rpcnne0 
|- ( A e. RR+ -> ( A e. CC /\ A =/= 0 ) )

Proof

Step Hyp Ref Expression
1 rpcn 
 |-  ( A e. RR+ -> A e. CC )
2 rpne0 
 |-  ( A e. RR+ -> A =/= 0 )
3 1 2 jca 
 |-  ( A e. RR+ -> ( A e. CC /\ A =/= 0 ) )