Metamath Proof Explorer

Theorem logcl

Description: Closure of the natural logarithm function. (Contributed by NM, 21-Apr-2008) (Revised by Mario Carneiro, 23-Sep-2014)

Ref Expression
Assertion logcl A A 0 log A


Step Hyp Ref Expression
1 logrncl A A 0 log A ran log
2 logrncn log A ran log log A
3 1 2 syl A A 0 log A