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	⊢ ( 𝜑 ↔ ¬ Prv 𝜑 )
	bj-godellob.1	⊢ ¬ Prv ⊥
Assertion	bj-godellob	⊢ ⊥

Proof

Step	Hyp	Ref	Expression
1		bj-godellob.s	⊢ ( 𝜑 ↔ ¬ Prv 𝜑 )
2		bj-godellob.1	⊢ ¬ Prv ⊥
3		dfnot	⊢ ( ¬ Prv 𝜑 ↔ ( Prv 𝜑 → ⊥ ) )
4	1 3	bitri	⊢ ( 𝜑 ↔ ( Prv 𝜑 → ⊥ ) )
5	2	pm2.21i	⊢ ( Prv ⊥ → ⊥ )
6	4 5	bj-babylob	⊢ ⊥