How to prove if $ f:A\to B$, then $ |A|\geq |f(A)|$?

Question

I tried to prove by contradiction.

$|A|<|f(A)|$:

That mean the number of image element of set A is more than the set A, there will have two image elements of set A connect to same element of set A, contradiction with the element of domain can only connect to exactly one element to codomain.

Therefore,$|A|≥|f(A)|.$ Am I right?