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

Proof

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