Show that if a_k is absolutely convergent and abs(b_k) abs(a_k) fopr all k, then b_k is absolutely convergent

Here is what I have for this:

Because abs(b_k) abs(a_k), then abs(b_k) abs(a_k)

With the basic comparison test, since abs(a_k) is convergent, then abs(b_k) is convergent

Since abs(b_k) is convergent, by theorem bk converges and is absolutely convergent.

Is this proof sufficient?