Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-godellob Structured version   Visualization version   GIF version

Theorem bj-godellob 32926
Description: Proof of Gödel's theorem from Löb's theorem (see comments at bj-babygodel 32924 and bj-babylob 32925 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 1650 . . 3 (¬ Prv 𝜑 ↔ (Prv 𝜑 → ⊥))
31, 2bitri 264 . 2 (𝜑 ↔ (Prv 𝜑 → ⊥))
4 bj-godellob.1 . . 3 ¬ Prv ⊥
54pm2.21i 117 . 2 (Prv ⊥ → ⊥)
63, 5bj-babylob 32925 1
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wfal 1636  Prv cprvb 32918
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-prv1 32919  ax-prv2 32920  ax-prv3 32921
This theorem depends on definitions:  df-bi 197  df-tru 1634  df-fal 1637
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator