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Theorem bj-godellob 31763
 Description: Proof of Gödel's theorem from Löb's theorem (see comments at bj-babygodel 31761 and bj-babylob 31762 for details). (Contributed by BJ, 20-Apr-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
bj-godellob.s (𝜑 ↔ ¬ Prv 𝜑)
bj-godellob.1 ¬ Prv ⊥
Assertion
Ref Expression
bj-godellob

Proof of Theorem bj-godellob
StepHypRef Expression
1 bj-godellob.s . . 3 (𝜑 ↔ ¬ Prv 𝜑)
2 dfnot 1493 . . 3 (¬ Prv 𝜑 ↔ (Prv 𝜑 → ⊥))
31, 2bitri 263 . 2 (𝜑 ↔ (Prv 𝜑 → ⊥))
4 bj-godellob.1 . . 3 ¬ Prv ⊥
54pm2.21i 115 . 2 (Prv ⊥ → ⊥)
63, 5bj-babylob 31762 1
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 195  ⊥wfal 1480  Prv cprvb 31755 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-prv1 31756  ax-prv2 31757  ax-prv3 31758 This theorem depends on definitions:  df-bi 196  df-tru 1478  df-fal 1481 This theorem is referenced by: (None)
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