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	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
Assertion	reeflogd	⊢ ( 𝜑 → ( exp ‘ ( log ‘ 𝐴 ) ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		relogcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
2		reeflog	⊢ ( 𝐴 ∈ ℝ+ → ( exp ‘ ( log ‘ 𝐴 ) ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( exp ‘ ( log ‘ 𝐴 ) ) = 𝐴 )