Hi guys. I came up with a "proof" for , where is a prime formula, which is obviously false. But what have I done wrong?

I'm using Church's first pure predicate calculus formulation, (found in §30).

Suppose is a prime formula. Then

(1) - premise

(2) - generalization (Church *301, §30).

Therefore . By the deduction theorem (Church *360, §36), it follows that . So

(3) - theorem (from above)

(4) - axiom (Church *304, §30)

(5) - 3,4,mp

(6) - 5, def. of

(7) - 6, equ. of

(8) - premise

(9) - 7,8,mp

(10) - 9, generalization (Church *301, §30)

(11) - axiom (Church *306, §30)

(12) - 10,11,mp

(13) - 12, generalization (Church *301, §30).

So , which by the deduction theorem (Church *360, §36) means . But clearly this is false! So where did I go wrong?

Thanks in advance!