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Theorem bj-godellob 33836
Description: Proof of Gödel's theorem from Löb's theorem (see comments at bj-babygodel 33834 and bj-babylob 33835 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 1547 . . 3 (¬ Prv 𝜑 ↔ (Prv 𝜑 → ⊥))
31, 2bitri 276 . 2 (𝜑 ↔ (Prv 𝜑 → ⊥))
4 bj-godellob.1 . . 3 ¬ Prv ⊥
54pm2.21i 119 . 2 (Prv ⊥ → ⊥)
63, 5bj-babylob 33835 1
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207  wfal 1540  Prv cprvb 33828
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-prv1 33829  ax-prv2 33830  ax-prv3 33831
This theorem depends on definitions:  df-bi 208  df-tru 1531  df-fal 1541
This theorem is referenced by: (None)
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