Theorem efcld

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

	Ref	Expression
Hypothesis	efcld.1	$$⊢\phi \to A\in ℂ$$
Assertion	efcld	$$⊢\phi \to {\mathrm{e}}^A\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		efcld.1	$$⊢\phi \to A\in ℂ$$
2		efcl	$$⊢A\in ℂ\to {\mathrm{e}}^A\in ℂ$$
3	1 2	syl	$$⊢\phi \to {\mathrm{e}}^A\in ℂ$$