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 ∈ ℂ → ( exp ‘ 𝐴 ) ≠ 0 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝐴 ∈ ℂ → 𝐴 ∈ ℂ )
2	1	efne0d	⊢ ( 𝐴 ∈ ℂ → ( exp ‘ 𝐴 ) ≠ 0 )