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

Proof

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