同位语和定语从句的问题

问题描述:

同位语和定语从句的问题
Elizabeth blackwell,the first woman medical doctor in the unites stateds,founded the new york infirmary,an institution that has always had a completely female medical staff!中的an institution是不是做infirmary的同位语啊?还是定语?

同位语,因为infirmary is an institution 医院(医务室)是一种机构
后面that has always had a completely female medical staff是定语从句,修饰an institution