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Theorem bj-godellob 33964
Description: Proof of Gödel's theorem from Löb's theorem (see comments at bj-babygodel 33962 and bj-babylob 33963 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 1557 . . 3 (¬ Prv 𝜑 ↔ (Prv 𝜑 → ⊥))
31, 2bitri 278 . 2 (𝜑 ↔ (Prv 𝜑 → ⊥))
4 bj-godellob.1 . . 3 ¬ Prv ⊥
54pm2.21i 119 . 2 (Prv ⊥ → ⊥)
63, 5bj-babylob 33963 1
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 209  wfal 1550  Prv cprvb 33956
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-prv1 33957  ax-prv2 33958  ax-prv3 33959
This theorem depends on definitions:  df-bi 210  df-tru 1541  df-fal 1551
This theorem is referenced by: (None)
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