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 

Note that $n\equiv 4 \pmod {14}$ is an even number. Thus it can’t be a prime.
