Question

which property does it belongs to

Answer 1

somebody theorems
there are 6 and
this is one of them

Answer 2

Conventionally,  we consider sets having only same types of elements. ie elements and sets are not mixed up. 
Here A is an element of B and B is a subset of C. Hence every element of B is also an element of C also. Thus A is an element of C. 
Consider the example: 
A={a}  ,  B={ b, {a}}  and
C={b, c, {a}}. Here A is an element of B and B is a subset of C and hence A is also an element of C. 
But such sets are avoided in the discussions of basic set theory as it leads to logical difficulties like Russel's Paradox.