Metamath Proof Explorer

Theorem recne0zi

Description: The reciprocal of a nonzero number is nonzero. (Contributed by NM, 14-May-1999)

Ref Expression
Hypothesis divclz.1 
|- A e. CC
Assertion recne0zi 
|- ( A =/= 0 -> ( 1 / A ) =/= 0 )

Proof

Step Hyp Ref Expression
1 divclz.1 
 |-  A e. CC
2 recne0 
 |-  ( ( A e. CC /\ A =/= 0 ) -> ( 1 / A ) =/= 0 )
3 1 2 mpan 
 |-  ( A =/= 0 -> ( 1 / A ) =/= 0 )