The mirror fanne/mt_mysql is the official basic image pulled, and then mysql is compiled and installed on it

From docker exec, we can see that mysql is installed in fanne/mt_mysql image.

The mirror mt/mysql is created through dockerfile. the mirror FROM fanne/mt_mysql is created, but there is no mysql application after it is created.
Why can’t mt/mysql mirror inherit fanne/mt_mysql mirror?
Dockerfile content
[root@localhostmt_mysql]# cat Dockerfile
FROM fanne/mt_mysql:5.5
MAINTAINER FANE