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Metamath Proof Explorer

Theorem logrncn

Description: The range of the natural logarithm function is a subset of the complex numbers. (Contributed by Mario Carneiro, 13-May-2014)

		Ref	Expression
	Assertion	logrncn	$⊢ A \in ran log \to A \in ℂ$

Step	Hyp	Ref	Expression
1		ellogrn	$⊢ A \in ran log \leftrightarrow (A \in ℂ \land - π < ℑ (A) \land ℑ (A) \leq π)$
2	1	simp1bi	$⊢ A \in ran log \to A \in ℂ$