Theorem bj-godellob 32590

Description: Proof of Gödel's theorem from Löb's theorem (see comments at bj-babygodel 32588 and bj-babylob 32589 for details). (Contributed by BJ, 20-Apr-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
bj-godellob	|- F.

Proof of Theorem bj-godellob

Step	Hyp	Ref	Expression
1		bj-godellob.s	. . 3 |- ( ph <-> -. Prv ph )
2		dfnot 1502	. . 3 |- ( -. Prv ph <-> (Prv ph -> F. ) )
3	1, 2	bitri 264	. 2 |- ( ph <-> (Prv ph -> F. ) )
4		bj-godellob.1	. . 3 |- -. Prv F.
5	4	pm2.21i 116	. 2 |- (Prv F. -> F. )
6	3, 5	bj-babylob 32589	1 |- F.

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   F. wfal 1488  Prv cprvb 32582

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-prv1 32583  ax-prv2 32584  ax-prv3 32585

This theorem depends on definitions:  df-bi 197  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)