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	$$⊢\phi \to A\in ℝ$$
Assertion	relogefd	$$⊢\phi \to \log {\mathrm{e}}^A=A$$

Proof

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