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	|- ( ph -> A e. RR )
Assertion	relogefd	|- ( ph -> ( log ` ( exp ` A ) ) = A )

Proof

Step	Hyp	Ref	Expression
1		relogefd.1	|- ( ph -> A e. RR )
2		relogef	|- ( A e. RR -> ( log ` ( exp ` A ) ) = A )
3	1 2	syl	|- ( ph -> ( log ` ( exp ` A ) ) = A )