Theorem efcld

Description: Closure law for the exponential function, deduction version. (Contributed by Thierry Arnoux, 1-Dec-2021)

	Ref	Expression
Hypothesis	efcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	efcld	⊢ ( 𝜑 → ( exp ‘ 𝐴 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		efcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		efcl	⊢ ( 𝐴 ∈ ℂ → ( exp ‘ 𝐴 ) ∈ ℂ )
3	1 2	syl	⊢ ( 𝜑 → ( exp ‘ 𝐴 ) ∈ ℂ )