From wikipedia I obtain the following definition of an injective function :
Let $f$ be a function whose domain is a set $A$. The function $f$ is injective if for all $a$ and $b$ in $A$, if $f(a) = f(b)$, then $a = b$; that is, $f(a) = f(b)$ implies $a = b$.
From this I conclude that a function $f$ is injective if the below statement is true for all $a,b \in A$:
$$f(a)=f(b) \implies a=b$$
My question is: Can I re-formulate the above statement as $f(a)=f(b) \iff a=b$ ?