Metamath Proof Explorer

Theorem relogcld

Description: Closure of the natural logarithm function. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis relogcld.1 
|- ( ph -> A e. RR+ )
Assertion relogcld 
|- ( ph -> ( log ` A ) e. RR )

Proof

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