Proof of Tarski's self-reference lemma

Question

In http://www.math.hawaii.edu/~dale/godel/godel.html, Tarksi's self reference lemma is mentioned but the proof is omitted.

Tarski's Self-Reference Lemma. For any formula $p(x)$ in an adequate theory, there is a sentence (formula without free variables) $s$ such that $s$ iff $p(<s>)$ where $<s>$ is the number which encodes $s$.

Can anyone show the reference to the proof, or the proof here?

Answer 1

See this lecture notes by Vann McGee.