If $p$ is a prime such that $p\equiv 4 \mod 7,$ then $p \equiv 4\mod 14.$ Prove or disprove :

If $p$ is a prime such that $p\equiv 4 \mod 7,$ then $p \equiv 4\mod 14.$

I think it is a false statement because if $p=11$ then $p\equiv 4 \mod 7$ but $p \not \equiv 4\mod 14.$
Is my counterexample correct?
thanks 

To add on to gimusi's answer, the proposition could still be correct even given that $n\equiv4\text{ (mod }14)$, but only if $p\equiv4\text{ (mod }7)$ was never true for any prime.
Your counterexample is a valid disproof of the original statement.
