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Metamath Proof Explorer

Theorem efcld

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

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

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