Metamath Proof Explorer


Theorem efne0

Description: The exponential of a complex number is nonzero. Corollary 15-4.3 of Gleason p. 309. (Contributed by NM, 13-Jan-2006) (Revised by Mario Carneiro, 29-Apr-2014) (Proof shortened by TA, 14-Nov-2025)

Ref Expression
Assertion efne0
|- ( A e. CC -> ( exp ` A ) =/= 0 )

Proof

Step Hyp Ref Expression
1 id
 |-  ( A e. CC -> A e. CC )
2 1 efne0d
 |-  ( A e. CC -> ( exp ` A ) =/= 0 )