Theorem bj-godellob

Description: Proof of Gödel's theorem from Löb's theorem (see comments at bj-babygodel and bj-babylob for details). (Contributed by BJ, 20-Apr-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bj-godellob.s	|- ( ph <-> -. Prv ph )
	bj-godellob.1	|- -. Prv F.
Assertion	bj-godellob	|- F.

Proof

Step	Hyp	Ref	Expression
1		bj-godellob.s	|- ( ph <-> -. Prv ph )
2		bj-godellob.1	|- -. Prv F.
3		dfnot	|- ( -. Prv ph <-> ( Prv ph -> F. ) )
4	1 3	bitri	|- ( ph <-> ( Prv ph -> F. ) )
5	2	pm2.21i	|- ( Prv F. -> F. )
6	4 5	bj-babylob	|- F.