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Metamath Proof Explorer

Theorem relogefd

Description: Relationship between the natural logarithm function and the exponential function. (Contributed by Mario Carneiro, 29-May-2016)

		Ref	Expression
	Hypothesis	relogefd.1	$⊢ φ \to A \in ℝ$
	Assertion	relogefd	$⊢ φ \to \log e^{A} = A$

Step	Hyp	Ref	Expression
1		relogefd.1	$⊢ φ \to A \in ℝ$
2		relogef	$⊢ A \in ℝ \to \log e^{A} = A$
3	1 2	syl	$⊢ φ \to \log e^{A} = A$