Metamath Proof Explorer

Theorem rpcndif0

Description: A positive real number is a complex number not being 0. (Contributed by AV, 29-May-2020)

Ref Expression
Assertion rpcndif0 
|- ( A e. RR+ -> A e. ( CC \ { 0 } ) )

Proof

Step Hyp Ref Expression
1 rpcnne0 
 |-  ( A e. RR+ -> ( A e. CC /\ A =/= 0 ) )
2 eldifsn 
 |-  ( A e. ( CC \ { 0 } ) <-> ( A e. CC /\ A =/= 0 ) )
3 1 2 sylibr 
 |-  ( A e. RR+ -> A e. ( CC \ { 0 } ) )