Sayam's Theorem of Primality

Ok. This is not really a theorem yet, more of a hypothesis. And someone else might have shown this before but I thought about it last night.

Every prime number contains atleast one digit that is itself, a prime number.

E.g. 2 is a prime number. And 2 happens to be a prime.
E.g. 29 is a prime number. And 2 in 29 is a prime.
E.g. 79 is a prime number. And 7 is a prime.

How can I prove it?