Theorem reeflogd

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

	Ref	Expression
Hypothesis	relogcld.1	$$⊢\phi \to A\in {ℝ}^{+}$$
Assertion	reeflogd	$$⊢\phi \to {\mathrm{e}}^{\log A}=A$$

Proof

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