Proving Proper Subsets Formally

[The Student]

Let A = {1} and B = {1, 2}. Prove that A is a subset of B. What would be a/the formal way to prove this?

 

[JohnZ]

A={student1}, B={student1, student2}, obviously A is contained in B, so A is subset of B.

 

[The Student]

A={student1}, B={student1, student2}, obviously A is contained in B, so A is subset of B.

But the question in the textbook wants a proof.

 

[JohnZ]

By definition:
If A and B are sets and every element of A is also an element of B, then:
A is a subset of B.