SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC

Hello can someone explain me exacty how in this fragment of the paper (SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC, RICHARDG.HECK,JR.):

• (9) Tr(x) ≡∃y(rhs(x,y)∧¬Tr(y)), where rhs(x,y) is a formula representing the relation: y is (Gödel number of) the right-hand side of the biconditional (whose Gödel number is) x. Diagonalization then yields a formula G such that PAs (Paeno arithmetic , 's' stands for standard language)

proves:

• (10) G≡[Tr(`G`)≡∃y(rhs(`G`,y)∧¬Tr(y))], where, as usual, `G` abbreviates the numeral denoting the Gödel number of the formula G.

How (10) can be derived from (9) trough Diagonalization?

• See e.g. Gödel’s Incompleteness Theorems. – Mauro ALLEGRANZA Oct 30 '19 at 13:33
• I don't see how following the steps of the "diagonalization lemma" referenced there takes one from (9) to (10) – Noname Oct 30 '19 at 13:40
• But then G in (10) must be equivalent to (9) , how then in (10) is it equivalent to the right-hand side of the equivalence(10)? – Noname Oct 30 '19 at 13:54